Submit Info #59525

Problem Lang User Status Time Memory
Polynomial Taylor Shift cpp-acl nok0 AC 191 ms 50.86 MiB

ケース詳細
Name Status Time Memory
example_00 AC 65 ms 34.78 MiB
example_01 AC 59 ms 34.70 MiB
fft_killer_00 AC 191 ms 50.82 MiB
fft_killer_01 AC 187 ms 50.86 MiB
max_random_00 AC 186 ms 50.75 MiB
max_random_01 AC 185 ms 50.81 MiB
medium_00 AC 58 ms 34.86 MiB
medium_01 AC 60 ms 35.02 MiB
medium_02 AC 59 ms 35.02 MiB
medium_all_zero_00 AC 58 ms 34.82 MiB
medium_c_zero_00 AC 63 ms 34.84 MiB
random_00 AC 171 ms 48.75 MiB
random_01 AC 183 ms 49.92 MiB
random_02 AC 74 ms 36.66 MiB
small_00 AC 62 ms 34.86 MiB
small_01 AC 66 ms 34.70 MiB
small_02 AC 66 ms 34.83 MiB
small_03 AC 62 ms 34.82 MiB
small_04 AC 65 ms 34.74 MiB
small_05 AC 61 ms 34.78 MiB
small_06 AC 62 ms 34.86 MiB
small_07 AC 59 ms 34.85 MiB
small_08 AC 58 ms 34.75 MiB
small_09 AC 59 ms 34.81 MiB
small_10 AC 62 ms 34.82 MiB
small_11 AC 62 ms 34.82 MiB
small_12 AC 61 ms 34.82 MiB
small_13 AC 61 ms 34.82 MiB
small_14 AC 62 ms 34.85 MiB
small_15 AC 60 ms 34.81 MiB

#line 1 "a.cpp" #define PROBLEM "https://judge.yosupo.jp/problem/polynomial_taylor_shift" #line 1 "/Users/nok0/Documents/Programming/nok0/atcoder/modint.hpp" #include <cassert> #include <numeric> #include <type_traits> #ifdef _MSC_VER #include <intrin.h> #endif #line 1 "/Users/nok0/Documents/Programming/nok0/atcoder/internal_math.hpp" #include <utility> #ifdef _MSC_VER #include <intrin.h> #endif namespace atcoder { namespace internal { // @param m `1 <= m` // @return x mod m constexpr long long safe_mod(long long x, long long m) { x %= m; if (x < 0) x += m; return x; } // Fast modular multiplication by barrett reduction // Reference: https://en.wikipedia.org/wiki/Barrett_reduction // NOTE: reconsider after Ice Lake struct barrett { unsigned int _m; unsigned long long im; // @param m `1 <= m < 2^31` explicit barrett(unsigned int m) : _m(m), im((unsigned long long)(-1) / m + 1) {} // @return m unsigned int umod() const { return _m; } // @param a `0 <= a < m` // @param b `0 <= b < m` // @return `a * b % m` unsigned int mul(unsigned int a, unsigned int b) const { // [1] m = 1 // a = b = im = 0, so okay // [2] m >= 2 // im = ceil(2^64 / m) // -> im * m = 2^64 + r (0 <= r < m) // let z = a*b = c*m + d (0 <= c, d < m) // a*b * im = (c*m + d) * im = c*(im*m) + d*im = c*2^64 + c*r + d*im // c*r + d*im < m * m + m * im < m * m + 2^64 + m <= 2^64 + m * (m + 1) < 2^64 * 2 // ((ab * im) >> 64) == c or c + 1 unsigned long long z = a; z *= b; #ifdef _MSC_VER unsigned long long x; _umul128(z, im, &x); #else unsigned long long x = (unsigned long long)(((unsigned __int128)(z)*im) >> 64); #endif unsigned int v = (unsigned int)(z - x * _m); if (_m <= v) v += _m; return v; } }; // @param n `0 <= n` // @param m `1 <= m` // @return `(x ** n) % m` constexpr long long pow_mod_constexpr(long long x, long long n, int m) { if (m == 1) return 0; unsigned int _m = (unsigned int)(m); unsigned long long r = 1; unsigned long long y = safe_mod(x, m); while (n) { if (n & 1) r = (r * y) % _m; y = (y * y) % _m; n >>= 1; } return r; } // Reference: // M. Forisek and J. Jancina, // Fast Primality Testing for Integers That Fit into a Machine Word // @param n `0 <= n` constexpr bool is_prime_constexpr(int n) { if (n <= 1) return false; if (n == 2 || n == 7 || n == 61) return true; if (n % 2 == 0) return false; long long d = n - 1; while (d % 2 == 0) d /= 2; constexpr long long bases[3] = {2, 7, 61}; for (long long a : bases) { long long t = d; long long y = pow_mod_constexpr(a, t, n); while (t != n - 1 && y != 1 && y != n - 1) { y = y * y % n; t <<= 1; } if (y != n - 1 && t % 2 == 0) { return false; } } return true; } template <int n> constexpr bool is_prime = is_prime_constexpr(n); // @param b `1 <= b` // @return pair(g, x) s.t. g = gcd(a, b), xa = g (mod b), 0 <= x < b/g constexpr std::pair<long long, long long> inv_gcd(long long a, long long b) { a = safe_mod(a, b); if (a == 0) return {b, 0}; // Contracts: // [1] s - m0 * a = 0 (mod b) // [2] t - m1 * a = 0 (mod b) // [3] s * |m1| + t * |m0| <= b long long s = b, t = a; long long m0 = 0, m1 = 1; while (t) { long long u = s / t; s -= t * u; m0 -= m1 * u; // |m1 * u| <= |m1| * s <= b // [3]: // (s - t * u) * |m1| + t * |m0 - m1 * u| // <= s * |m1| - t * u * |m1| + t * (|m0| + |m1| * u) // = s * |m1| + t * |m0| <= b auto tmp = s; s = t; t = tmp; tmp = m0; m0 = m1; m1 = tmp; } // by [3]: |m0| <= b/g // by g != b: |m0| < b/g if (m0 < 0) m0 += b / s; return {s, m0}; } // Compile time primitive root // @param m must be prime // @return primitive root (and minimum in now) constexpr int primitive_root_constexpr(int m) { if (m == 2) return 1; if (m == 167772161) return 3; if (m == 469762049) return 3; if (m == 754974721) return 11; if (m == 998244353) return 3; int divs[20] = {}; divs[0] = 2; int cnt = 1; int x = (m - 1) / 2; while (x % 2 == 0) x /= 2; for (int i = 3; (long long)(i)*i <= x; i += 2) { if (x % i == 0) { divs[cnt++] = i; while (x % i == 0) { x /= i; } } } if (x > 1) { divs[cnt++] = x; } for (int g = 2;; g++) { bool ok = true; for (int i = 0; i < cnt; i++) { if (pow_mod_constexpr(g, (m - 1) / divs[i], m) == 1) { ok = false; break; } } if (ok) return g; } } template <int m> constexpr int primitive_root = primitive_root_constexpr(m); // @param n `n < 2^32` // @param m `1 <= m < 2^32` // @return sum_{i=0}^{n-1} floor((ai + b) / m) (mod 2^64) unsigned long long floor_sum_unsigned(unsigned long long n, unsigned long long m, unsigned long long a, unsigned long long b) { unsigned long long ans = 0; while (true) { if (a >= m) { ans += n * (n - 1) / 2 * (a / m); a %= m; } if (b >= m) { ans += n * (b / m); b %= m; } unsigned long long y_max = a * n + b; if (y_max < m) break; // y_max < m * (n + 1) // floor(y_max / m) <= n n = (unsigned long long)(y_max / m); b = (unsigned long long)(y_max % m); std::swap(m, a); } return ans; } } // namespace internal } // namespace atcoder #line 1 "/Users/nok0/Documents/Programming/nok0/atcoder/internal_type_traits.hpp" #line 7 "/Users/nok0/Documents/Programming/nok0/atcoder/internal_type_traits.hpp" namespace atcoder { namespace internal { #ifndef _MSC_VER template <class T> using is_signed_int128 = typename std::conditional<std::is_same<T, __int128_t>::value || std::is_same<T, __int128>::value, std::true_type, std::false_type>::type; template <class T> using is_unsigned_int128 = typename std::conditional<std::is_same<T, __uint128_t>::value || std::is_same<T, unsigned __int128>::value, std::true_type, std::false_type>::type; template <class T> using make_unsigned_int128 = typename std::conditional<std::is_same<T, __int128_t>::value, __uint128_t, unsigned __int128>; template <class T> using is_integral = typename std::conditional<std::is_integral<T>::value || is_signed_int128<T>::value || is_unsigned_int128<T>::value, std::true_type, std::false_type>::type; template <class T> using is_signed_int = typename std::conditional<(is_integral<T>::value && std::is_signed<T>::value) || is_signed_int128<T>::value, std::true_type, std::false_type>::type; template <class T> using is_unsigned_int = typename std::conditional<(is_integral<T>::value && std::is_unsigned<T>::value) || is_unsigned_int128<T>::value, std::true_type, std::false_type>::type; template <class T> using to_unsigned = typename std::conditional< is_signed_int128<T>::value, make_unsigned_int128<T>, typename std::conditional<std::is_signed<T>::value, std::make_unsigned<T>, std::common_type<T>>::type>::type; #else template <class T> using is_integral = typename std::is_integral<T>; template <class T> using is_signed_int = typename std::conditional<is_integral<T>::value && std::is_signed<T>::value, std::true_type, std::false_type>::type; template <class T> using is_unsigned_int = typename std::conditional<is_integral<T>::value && std::is_unsigned<T>::value, std::true_type, std::false_type>::type; template <class T> using to_unsigned = typename std::conditional<is_signed_int<T>::value, std::make_unsigned<T>, std::common_type<T>>::type; #endif template <class T> using is_signed_int_t = std::enable_if_t<is_signed_int<T>::value>; template <class T> using is_unsigned_int_t = std::enable_if_t<is_unsigned_int<T>::value>; template <class T> using to_unsigned_t = typename to_unsigned<T>::type; } // namespace internal } // namespace atcoder #line 14 "/Users/nok0/Documents/Programming/nok0/atcoder/modint.hpp" namespace atcoder { namespace internal { struct modint_base {}; struct static_modint_base : modint_base {}; template <class T> using is_modint = std::is_base_of<modint_base, T>; template <class T> using is_modint_t = std::enable_if_t<is_modint<T>::value>; } // namespace internal template <int m, std::enable_if_t<(1 <= m)>* = nullptr> struct static_modint : internal::static_modint_base { using mint = static_modint; public: static constexpr int mod() { return m; } static mint raw(int v) { mint x; x._v = v; return x; } static_modint() : _v(0) {} template <class T, internal::is_signed_int_t<T>* = nullptr> static_modint(T v) { long long x = (long long)(v % (long long)(umod())); if (x < 0) x += umod(); _v = (unsigned int)(x); } template <class T, internal::is_unsigned_int_t<T>* = nullptr> static_modint(T v) { _v = (unsigned int)(v % umod()); } unsigned int val() const { return _v; } mint& operator++() { _v++; if (_v == umod()) _v = 0; return *this; } mint& operator--() { if (_v == 0) _v = umod(); _v--; return *this; } mint operator++(int) { mint result = *this; ++*this; return result; } mint operator--(int) { mint result = *this; --*this; return result; } mint& operator+=(const mint& rhs) { _v += rhs._v; if (_v >= umod()) _v -= umod(); return *this; } mint& operator-=(const mint& rhs) { _v -= rhs._v; if (_v >= umod()) _v += umod(); return *this; } mint& operator*=(const mint& rhs) { unsigned long long z = _v; z *= rhs._v; _v = (unsigned int)(z % umod()); return *this; } mint& operator/=(const mint& rhs) { return *this = *this * rhs.inv(); } mint operator+() const { return *this; } mint operator-() const { return mint() - *this; } mint pow(long long n) const { assert(0 <= n); mint x = *this, r = 1; while (n) { if (n & 1) r *= x; x *= x; n >>= 1; } return r; } mint inv() const { if (prime) { assert(_v); return pow(umod() - 2); } else { auto eg = internal::inv_gcd(_v, m); assert(eg.first == 1); return eg.second; } } friend mint operator+(const mint& lhs, const mint& rhs) { return mint(lhs) += rhs; } friend mint operator-(const mint& lhs, const mint& rhs) { return mint(lhs) -= rhs; } friend mint operator*(const mint& lhs, const mint& rhs) { return mint(lhs) *= rhs; } friend mint operator/(const mint& lhs, const mint& rhs) { return mint(lhs) /= rhs; } friend bool operator==(const mint& lhs, const mint& rhs) { return lhs._v == rhs._v; } friend bool operator!=(const mint& lhs, const mint& rhs) { return lhs._v != rhs._v; } private: unsigned int _v; static constexpr unsigned int umod() { return m; } static constexpr bool prime = internal::is_prime<m>; }; template <int id> struct dynamic_modint : internal::modint_base { using mint = dynamic_modint; public: static int mod() { return (int)(bt.umod()); } static void set_mod(int m) { assert(1 <= m); bt = internal::barrett(m); } static mint raw(int v) { mint x; x._v = v; return x; } dynamic_modint() : _v(0) {} template <class T, internal::is_signed_int_t<T>* = nullptr> dynamic_modint(T v) { long long x = (long long)(v % (long long)(mod())); if (x < 0) x += mod(); _v = (unsigned int)(x); } template <class T, internal::is_unsigned_int_t<T>* = nullptr> dynamic_modint(T v) { _v = (unsigned int)(v % mod()); } unsigned int val() const { return _v; } mint& operator++() { _v++; if (_v == umod()) _v = 0; return *this; } mint& operator--() { if (_v == 0) _v = umod(); _v--; return *this; } mint operator++(int) { mint result = *this; ++*this; return result; } mint operator--(int) { mint result = *this; --*this; return result; } mint& operator+=(const mint& rhs) { _v += rhs._v; if (_v >= umod()) _v -= umod(); return *this; } mint& operator-=(const mint& rhs) { _v += mod() - rhs._v; if (_v >= umod()) _v -= umod(); return *this; } mint& operator*=(const mint& rhs) { _v = bt.mul(_v, rhs._v); return *this; } mint& operator/=(const mint& rhs) { return *this = *this * rhs.inv(); } mint operator+() const { return *this; } mint operator-() const { return mint() - *this; } mint pow(long long n) const { assert(0 <= n); mint x = *this, r = 1; while (n) { if (n & 1) r *= x; x *= x; n >>= 1; } return r; } mint inv() const { auto eg = internal::inv_gcd(_v, mod()); assert(eg.first == 1); return eg.second; } friend mint operator+(const mint& lhs, const mint& rhs) { return mint(lhs) += rhs; } friend mint operator-(const mint& lhs, const mint& rhs) { return mint(lhs) -= rhs; } friend mint operator*(const mint& lhs, const mint& rhs) { return mint(lhs) *= rhs; } friend mint operator/(const mint& lhs, const mint& rhs) { return mint(lhs) /= rhs; } friend bool operator==(const mint& lhs, const mint& rhs) { return lhs._v == rhs._v; } friend bool operator!=(const mint& lhs, const mint& rhs) { return lhs._v != rhs._v; } private: unsigned int _v; static internal::barrett bt; static unsigned int umod() { return bt.umod(); } }; template <int id> internal::barrett dynamic_modint<id>::bt(998244353); using modint998244353 = static_modint<998244353>; using modint1000000007 = static_modint<1000000007>; using modint = dynamic_modint<-1>; namespace internal { template <class T> using is_static_modint = std::is_base_of<internal::static_modint_base, T>; template <class T> using is_static_modint_t = std::enable_if_t<is_static_modint<T>::value>; template <class> struct is_dynamic_modint : public std::false_type {}; template <int id> struct is_dynamic_modint<dynamic_modint<id>> : public std::true_type {}; template <class T> using is_dynamic_modint_t = std::enable_if_t<is_dynamic_modint<T>::value>; } // namespace internal } // namespace atcoder #line 1 "/Users/nok0/Documents/Programming/nok0/cftemp.hpp" #include <bits/stdc++.h> using namespace std; #pragma region Macros // rep macro #define foa(v, a) for(auto &v : a) #define REPname(a, b, c, d, e, ...) e #define REP(...) REPname(__VA_ARGS__, REP3, REP2, REP1, REP0)(__VA_ARGS__) #define REP0(x) for(int i = 0; i < (x); ++i) #define REP1(i, x) for(int i = 0; i < (x); ++i) #define REP2(i, l, r) for(int i = (l); i < (r); ++i) #define REP3(i, l, r, c) for(int i = (l); i < (r); i += (c)) #define REPSname(a, b, c, ...) c #define REPS(...) REPSname(__VA_ARGS__, REPS1, REPS0)(__VA_ARGS__) #define REPS0(x) for(int i = 1; i <= (x); ++i) #define REPS1(i, x) for(int i = 1; i <= (x); ++i) #define RREPname(a, b, c, d, e, ...) e #define RREP(...) RREPname(__VA_ARGS__, RREP3, RREP2, RREP1, RREP0)(__VA_ARGS__) #define RREP0(x) for(int i = (x)-1; i >= 0; --i) #define RREP1(i, x) for(int i = (x)-1; i >= 0; --i) #define RREP2(i, r, l) for(int i = (r)-1; i >= (l); --i) #define RREP3(i, r, l, c) for(int i = (r)-1; i >= (l); i -= (c)) #define RREPSname(a, b, c, ...) c #define RREPS(...) RREPSname(__VA_ARGS__, RREPS1, RREPS0)(__VA_ARGS__) #define RREPS0(x) for(int i = (x); i >= 1; --i) #define RREPS1(i, x) for(int i = (x); i >= 1; --i) // name macro #define pb push_back #define eb emplace_back #define SZ(x) ((int)(x).size()) #define all(x) (x).begin(), (x).end() #define rall(x) (x).rbegin(), (x).rend() #define popcnt(x) __builtin_popcountll(x) template <class T = int> using V = std::vector<T>; template <class T = int> using VV = std::vector<std::vector<T>>; template <class T> using pqup = std::priority_queue<T, std::vector<T>, std::greater<T>>; using ll = long long; using ld = long double; using int128 = __int128_t; using pii = std::pair<int, int>; using pll = std::pair<long long, long long>; // input macro template <class T, class U> std::istream &operator>>(std::istream &is, std::pair<T, U> &p) { is >> p.first >> p.second; return is; } template <class T> std::istream &operator>>(std::istream &is, std::vector<T> &v) { for(T &i : v) is >> i; return is; } std::istream &operator>>(std::istream &is, __int128_t &a) { std::string s; is >> s; __int128_t ret = 0; for(int i = 0; i < s.length(); i++) if('0' <= s[i] and s[i] <= '9') ret = 10 * ret + s[i] - '0'; a = ret * (s[0] == '-' ? -1 : 1); return is; } namespace scanner { void scan(int &a) { std::cin >> a; } void scan(long long &a) { std::cin >> a; } void scan(std::string &a) { std::cin >> a; } void scan(char &a) { std::cin >> a; } void scan(char a[]) { std::scanf("%s", a); } void scan(double &a) { std::cin >> a; } void scan(long double &a) { std::cin >> a; } template <class T, class U> void scan(std::pair<T, U> &p) { std::cin >> p; } template <class T> void scan(std::vector<T> &a) { std::cin >> a; } void INPUT() {} template <class Head, class... Tail> void INPUT(Head &head, Tail &... tail) { scan(head); INPUT(tail...); } } // namespace scanner #define VEC(type, name, size) \ std::vector<type> name(size); \ scanner::INPUT(name) #define VVEC(type, name, h, w) \ std::vector<std::vector<type>> name(h, std::vector<type>(w)); \ scanner::INPUT(name) #define INT(...) \ int __VA_ARGS__; \ scanner::INPUT(__VA_ARGS__) #define LL(...) \ long long __VA_ARGS__; \ scanner::INPUT(__VA_ARGS__) #define STR(...) \ std::string __VA_ARGS__; \ scanner::INPUT(__VA_ARGS__) #define CHAR(...) \ char __VA_ARGS__; \ scanner::INPUT(__VA_ARGS__) #define DOUBLE(...) \ double __VA_ARGS__; \ scanner::INPUT(__VA_ARGS__) #define LD(...) \ long double __VA_ARGS__; \ scanner::INPUT(__VA_ARGS__) // output-macro template <class T, class U> std::ostream &operator<<(std::ostream &os, const std::pair<T, U> &p) { os << p.first << " " << p.second; return os; } template <class T> std::ostream &operator<<(std::ostream &os, const std::vector<T> &a) { for(int i = 0; i < int(a.size()); ++i) { if(i) os << " "; os << a[i]; } return os; } std::ostream &operator<<(std::ostream &dest, __int128_t &value) { std::ostream::sentry s(dest); if(s) { __uint128_t tmp = value < 0 ? -value : value; char buffer[128]; char *d = std::end(buffer); do { --d; *d = "0123456789"[tmp % 10]; tmp /= 10; } while(tmp != 0); if(value < 0) { --d; *d = '-'; } int len = std::end(buffer) - d; if(dest.rdbuf()->sputn(d, len) != len) { dest.setstate(std::ios_base::badbit); } } return dest; } template <class T> void print(const T a) { std::cout << a << '\n'; } template <class Head, class... Tail> void print(Head H, Tail... T) { std::cout << H << ' '; print(T...); } template <class T> void printel(const T a) { std::cout << a << '\n'; } template <class T> void printel(const std::vector<T> &a) { for(const auto &v : a) std::cout << v << '\n'; } template <class Head, class... Tail> void printel(Head H, Tail... T) { std::cout << H << '\n'; printel(T...); } void Yes(const bool b = true) { std::cout << (b ? "Yes\n" : "No\n"); } void No() { std::cout << "No\n"; } void YES(const bool b = true) { std::cout << (b ? "YES\n" : "NO\n"); } void NO() { std::cout << "NO\n"; } void err(const bool b = true) { if(b) { std::cout << "-1\n", exit(0); } } //debug macro namespace debugger { template <class T> void view(const std::vector<T> &a) { std::cerr << "{ "; for(const auto &v : a) { std::cerr << v << ", "; } std::cerr << "\b\b }"; } template <class T> void view(const std::vector<std::vector<T>> &a) { std::cerr << "{\n"; for(const auto &v : a) { std::cerr << "\t"; view(v); std::cerr << "\n"; } std::cerr << "}"; } template <class T, class U> void view(const std::vector<std::pair<T, U>> &a) { std::cerr << "{\n"; for(const auto &p : a) std::cerr << "\t(" << p.first << ", " << p.second << ")\n"; std::cerr << "}"; } template <class T, class U> void view(const std::map<T, U> &m) { std::cerr << "{\n"; for(const auto &p : m) std::cerr << "\t[" << p.first << "] : " << p.second << "\n"; std::cerr << "}"; } template <class T, class U> void view(const std::pair<T, U> &p) { std::cerr << "(" << p.first << ", " << p.second << ")"; } template <class T> void view(const std::set<T> &s) { std::cerr << "{ "; for(auto &v : s) { view(v); std::cerr << ", "; } std::cerr << "\b\b }"; } template <class T> void view(const T &e) { std::cerr << e; } } // namespace debugger #ifdef LOCAL void debug_out() {} template <typename Head, typename... Tail> void debug_out(Head H, Tail... T) { debugger::view(H); std::cerr << ", "; debug_out(T...); } #define debug(...) \ do { \ std::cerr << __LINE__ << " [" << #__VA_ARGS__ << "] : ["; \ debug_out(__VA_ARGS__); \ std::cerr << "\b\b]\n"; \ } while(false) #else #define debug(...) (void(0)) #endif // vector macro template <class T> int lb(const std::vector<T> &a, const T x) { return std::distance((a).begin(), std::lower_bound((a).begin(), (a).end(), (x))); } template <class T> int ub(const std::vector<T> &a, const T x) { return std::distance((a).begin(), std::upper_bound((a).begin(), (a).end(), (x))); } template <class T> void UNIQUE(std::vector<T> &a) { std::sort(a.begin(), a.end()); a.erase(std::unique(a.begin(), a.end()), a.end()); } template <class T> std::vector<T> press(std::vector<T> &a) { auto res = a; UNIQUE(res); for(auto &v : a) v = lb(res, v); return res; } #define SORTname(a, b, c, ...) c #define SORT(...) SORTname(__VA_ARGS__, SORT1, SORT0, ...)(__VA_ARGS__) #define SORT0(a) std::sort((a).begin(), (a).end()) #define SORT1(a, c) std::sort((a).begin(), (a).end(), [](const auto x, const auto y) { return x c y; }) template <class T> void ADD(std::vector<T> &a, const T x = 1) { for(auto &v : a) v += x; } template <class T> void SUB(std::vector<T> &a, const T x = 1) { for(auto &v : a) v -= x; } template <class T> void MUL(std::vector<T> &a, const T x) { for(auto &v : a) v *= x; } template <class T> void DIV(std::vector<T> &a, const T x) { for(auto &v : a) v /= x; } std::vector<std::pair<char, int>> rle(const string &s) { int n = s.size(); std::vector<std::pair<char, int>> ret; for(int l = 0; l < n;) { int r = l + 1; for(; r < n and s[l] == s[r]; r++) {} ret.emplace_back(s[l], r - l); l = r; } return ret; } template <class T> std::vector<std::pair<T, int>> rle(const std::vector<T> &v) { int n = v.size(); std::vector<std::pair<T, int>> ret; for(int l = 0; l < n;) { int r = l + 1; for(; r < n and v[l] == v[r]; r++) {} ret.emplace_back(v[l], r - l); l = r; } return ret; } // math macro template <class T, class U> inline bool chmin(T &a, const U &b) { return a > b ? a = b, true : false; } template <class T, class U> inline bool chmax(T &a, const U &b) { return a < b ? a = b, true : false; } template <class T> T divup(T x, T y) { return (x + y - 1) / y; } template <class T> T POW(T a, long long n) { T ret = 1; while(n) { if(n & 1) ret *= a; a *= a; n >>= 1; } return ret; } // modpow long long POW(long long a, long long n, const int mod) { long long ret = 1; a = (a % mod + mod) % mod; while(n) { if(n & 1) (ret *= a) %= mod; (a *= a) %= mod; n >>= 1; } return ret; } // others struct fast_io { fast_io() { ios::sync_with_stdio(false); cin.tie(nullptr); cout << fixed << setprecision(15); } } fast_io_; const int inf = 1e9; const ll INF = 1e18; #pragma endregion void main_(); int main() { main_(); return 0; } #line 6 "/Users/nok0/Documents/Programming/nok0/math/formal_power_series.hpp" #line 1 "/Users/nok0/Documents/Programming/nok0/atcoder/convolution.hpp" #line 9 "/Users/nok0/Documents/Programming/nok0/atcoder/convolution.hpp" #line 1 "/Users/nok0/Documents/Programming/nok0/atcoder/internal_bit.hpp" #ifdef _MSC_VER #include <intrin.h> #endif namespace atcoder { namespace internal { // @param n `0 <= n` // @return minimum non-negative `x` s.t. `n <= 2**x` int ceil_pow2(int n) { int x = 0; while ((1U << x) < (unsigned int)(n)) x++; return x; } // @param n `1 <= n` // @return minimum non-negative `x` s.t. `(n & (1 << x)) != 0` constexpr int bsf_constexpr(unsigned int n) { int x = 0; while (!(n & (1 << x))) x++; return x; } // @param n `1 <= n` // @return minimum non-negative `x` s.t. `(n & (1 << x)) != 0` int bsf(unsigned int n) { #ifdef _MSC_VER unsigned long index; _BitScanForward(&index, n); return index; #else return __builtin_ctz(n); #endif } } // namespace internal } // namespace atcoder #line 12 "/Users/nok0/Documents/Programming/nok0/atcoder/convolution.hpp" namespace atcoder { namespace internal { template <class mint, int g = internal::primitive_root<mint::mod()>, internal::is_static_modint_t<mint>* = nullptr> struct fft_info { static constexpr int rank2 = bsf_constexpr(mint::mod() - 1); std::array<mint, rank2 + 1> root; // root[i]^(2^i) == 1 std::array<mint, rank2 + 1> iroot; // root[i] * iroot[i] == 1 std::array<mint, std::max(0, rank2 - 2 + 1)> rate2; std::array<mint, std::max(0, rank2 - 2 + 1)> irate2; std::array<mint, std::max(0, rank2 - 3 + 1)> rate3; std::array<mint, std::max(0, rank2 - 3 + 1)> irate3; fft_info() { root[rank2] = mint(g).pow((mint::mod() - 1) >> rank2); iroot[rank2] = root[rank2].inv(); for (int i = rank2 - 1; i >= 0; i--) { root[i] = root[i + 1] * root[i + 1]; iroot[i] = iroot[i + 1] * iroot[i + 1]; } { mint prod = 1, iprod = 1; for (int i = 0; i <= rank2 - 2; i++) { rate2[i] = root[i + 2] * prod; irate2[i] = iroot[i + 2] * iprod; prod *= iroot[i + 2]; iprod *= root[i + 2]; } } { mint prod = 1, iprod = 1; for (int i = 0; i <= rank2 - 3; i++) { rate3[i] = root[i + 3] * prod; irate3[i] = iroot[i + 3] * iprod; prod *= iroot[i + 3]; iprod *= root[i + 3]; } } } }; template <class mint, internal::is_static_modint_t<mint>* = nullptr> void butterfly(std::vector<mint>& a) { int n = int(a.size()); int h = internal::ceil_pow2(n); static const fft_info<mint> info; int len = 0; // a[i, i+(n>>len), i+2*(n>>len), ..] is transformed while (len < h) { if (h - len == 1) { int p = 1 << (h - len - 1); mint rot = 1; for (int s = 0; s < (1 << len); s++) { int offset = s << (h - len); for (int i = 0; i < p; i++) { auto l = a[i + offset]; auto r = a[i + offset + p] * rot; a[i + offset] = l + r; a[i + offset + p] = l - r; } if (s + 1 != (1 << len)) rot *= info.rate2[bsf(~(unsigned int)(s))]; } len++; } else { // 4-base int p = 1 << (h - len - 2); mint rot = 1, imag = info.root[2]; for (int s = 0; s < (1 << len); s++) { mint rot2 = rot * rot; mint rot3 = rot2 * rot; int offset = s << (h - len); for (int i = 0; i < p; i++) { auto mod2 = 1ULL * mint::mod() * mint::mod(); auto a0 = 1ULL * a[i + offset].val(); auto a1 = 1ULL * a[i + offset + p].val() * rot.val(); auto a2 = 1ULL * a[i + offset + 2 * p].val() * rot2.val(); auto a3 = 1ULL * a[i + offset + 3 * p].val() * rot3.val(); auto a1na3imag = 1ULL * mint(a1 + mod2 - a3).val() * imag.val(); auto na2 = mod2 - a2; a[i + offset] = a0 + a2 + a1 + a3; a[i + offset + 1 * p] = a0 + a2 + (2 * mod2 - (a1 + a3)); a[i + offset + 2 * p] = a0 + na2 + a1na3imag; a[i + offset + 3 * p] = a0 + na2 + (mod2 - a1na3imag); } if (s + 1 != (1 << len)) rot *= info.rate3[bsf(~(unsigned int)(s))]; } len += 2; } } } template <class mint, internal::is_static_modint_t<mint>* = nullptr> void butterfly_inv(std::vector<mint>& a) { int n = int(a.size()); int h = internal::ceil_pow2(n); static const fft_info<mint> info; int len = h; // a[i, i+(n>>len), i+2*(n>>len), ..] is transformed while (len) { if (len == 1) { int p = 1 << (h - len); mint irot = 1; for (int s = 0; s < (1 << (len - 1)); s++) { int offset = s << (h - len + 1); for (int i = 0; i < p; i++) { auto l = a[i + offset]; auto r = a[i + offset + p]; a[i + offset] = l + r; a[i + offset + p] = (unsigned long long)(mint::mod() + l.val() - r.val()) * irot.val(); ; } if (s + 1 != (1 << (len - 1))) irot *= info.irate2[bsf(~(unsigned int)(s))]; } len--; } else { // 4-base int p = 1 << (h - len); mint irot = 1, iimag = info.iroot[2]; for (int s = 0; s < (1 << (len - 2)); s++) { mint irot2 = irot * irot; mint irot3 = irot2 * irot; int offset = s << (h - len + 2); for (int i = 0; i < p; i++) { auto a0 = 1ULL * a[i + offset + 0 * p].val(); auto a1 = 1ULL * a[i + offset + 1 * p].val(); auto a2 = 1ULL * a[i + offset + 2 * p].val(); auto a3 = 1ULL * a[i + offset + 3 * p].val(); auto a2na3iimag = 1ULL * mint((mint::mod() + a2 - a3) * iimag.val()).val(); a[i + offset] = a0 + a1 + a2 + a3; a[i + offset + 1 * p] = (a0 + (mint::mod() - a1) + a2na3iimag) * irot.val(); a[i + offset + 2 * p] = (a0 + a1 + (mint::mod() - a2) + (mint::mod() - a3)) * irot2.val(); a[i + offset + 3 * p] = (a0 + (mint::mod() - a1) + (mint::mod() - a2na3iimag)) * irot3.val(); } if (s + 1 != (1 << (len - 2))) irot *= info.irate3[bsf(~(unsigned int)(s))]; } len -= 2; } } } template <class mint, internal::is_static_modint_t<mint>* = nullptr> std::vector<mint> convolution_naive(const std::vector<mint>& a, const std::vector<mint>& b) { int n = int(a.size()), m = int(b.size()); std::vector<mint> ans(n + m - 1); if (n < m) { for (int j = 0; j < m; j++) { for (int i = 0; i < n; i++) { ans[i + j] += a[i] * b[j]; } } } else { for (int i = 0; i < n; i++) { for (int j = 0; j < m; j++) { ans[i + j] += a[i] * b[j]; } } } return ans; } template <class mint, internal::is_static_modint_t<mint>* = nullptr> std::vector<mint> convolution_fft(std::vector<mint> a, std::vector<mint> b) { int n = int(a.size()), m = int(b.size()); int z = 1 << internal::ceil_pow2(n + m - 1); a.resize(z); internal::butterfly(a); b.resize(z); internal::butterfly(b); for (int i = 0; i < z; i++) { a[i] *= b[i]; } internal::butterfly_inv(a); a.resize(n + m - 1); mint iz = mint(z).inv(); for (int i = 0; i < n + m - 1; i++) a[i] *= iz; return a; } } // namespace internal template <class mint, internal::is_static_modint_t<mint>* = nullptr> std::vector<mint> convolution(std::vector<mint>&& a, std::vector<mint>&& b) { int n = int(a.size()), m = int(b.size()); if (!n || !m) return {}; if (std::min(n, m) <= 60) return convolution_naive(a, b); return internal::convolution_fft(a, b); } template <class mint, internal::is_static_modint_t<mint>* = nullptr> std::vector<mint> convolution(const std::vector<mint>& a, const std::vector<mint>& b) { int n = int(a.size()), m = int(b.size()); if (!n || !m) return {}; if (std::min(n, m) <= 60) return convolution_naive(a, b); return internal::convolution_fft(a, b); } template <unsigned int mod = 998244353, class T, std::enable_if_t<internal::is_integral<T>::value>* = nullptr> std::vector<T> convolution(const std::vector<T>& a, const std::vector<T>& b) { int n = int(a.size()), m = int(b.size()); if (!n || !m) return {}; using mint = static_modint<mod>; std::vector<mint> a2(n), b2(m); for (int i = 0; i < n; i++) { a2[i] = mint(a[i]); } for (int i = 0; i < m; i++) { b2[i] = mint(b[i]); } auto c2 = convolution(move(a2), move(b2)); std::vector<T> c(n + m - 1); for (int i = 0; i < n + m - 1; i++) { c[i] = c2[i].val(); } return c; } std::vector<long long> convolution_ll(const std::vector<long long>& a, const std::vector<long long>& b) { int n = int(a.size()), m = int(b.size()); if (!n || !m) return {}; static constexpr unsigned long long MOD1 = 754974721; // 2^24 static constexpr unsigned long long MOD2 = 167772161; // 2^25 static constexpr unsigned long long MOD3 = 469762049; // 2^26 static constexpr unsigned long long M2M3 = MOD2 * MOD3; static constexpr unsigned long long M1M3 = MOD1 * MOD3; static constexpr unsigned long long M1M2 = MOD1 * MOD2; static constexpr unsigned long long M1M2M3 = MOD1 * MOD2 * MOD3; static constexpr unsigned long long i1 = internal::inv_gcd(MOD2 * MOD3, MOD1).second; static constexpr unsigned long long i2 = internal::inv_gcd(MOD1 * MOD3, MOD2).second; static constexpr unsigned long long i3 = internal::inv_gcd(MOD1 * MOD2, MOD3).second; auto c1 = convolution<MOD1>(a, b); auto c2 = convolution<MOD2>(a, b); auto c3 = convolution<MOD3>(a, b); std::vector<long long> c(n + m - 1); for (int i = 0; i < n + m - 1; i++) { unsigned long long x = 0; x += (c1[i] * i1) % MOD1 * M2M3; x += (c2[i] * i2) % MOD2 * M1M3; x += (c3[i] * i3) % MOD3 * M1M2; // B = 2^63, -B <= x, r(real value) < B // (x, x - M, x - 2M, or x - 3M) = r (mod 2B) // r = c1[i] (mod MOD1) // focus on MOD1 // r = x, x - M', x - 2M', x - 3M' (M' = M % 2^64) (mod 2B) // r = x, // x - M' + (0 or 2B), // x - 2M' + (0, 2B or 4B), // x - 3M' + (0, 2B, 4B or 6B) (without mod!) // (r - x) = 0, (0) // - M' + (0 or 2B), (1) // -2M' + (0 or 2B or 4B), (2) // -3M' + (0 or 2B or 4B or 6B) (3) (mod MOD1) // we checked that // ((1) mod MOD1) mod 5 = 2 // ((2) mod MOD1) mod 5 = 3 // ((3) mod MOD1) mod 5 = 4 long long diff = c1[i] - internal::safe_mod((long long)(x), (long long)(MOD1)); if (diff < 0) diff += MOD1; static constexpr unsigned long long offset[5] = { 0, 0, M1M2M3, 2 * M1M2M3, 3 * M1M2M3}; x -= offset[diff % 5]; c[i] = x; } return c; } } // namespace atcoder #line 3 "/Users/nok0/Documents/Programming/nok0/math/factorial.hpp" #line 5 "/Users/nok0/Documents/Programming/nok0/math/factorial.hpp" template <class T> struct factorial { public: static int MAX; static std::vector<T> fac, finv, inv; factorial() {} T binom(int n, int r) { if(n < r or n < 0 or r < 0) return T(0); assert(n < MAX); return fac[n] * finv[r] * finv[n - r]; } T large_binom(int n, int r) { if(n < r or n < 0 or r < 0) return T(0); assert(r < MAX); T ret = finv[r]; for(int i = 1; i <= r; ++i) ret *= (n + 1 - i); return ret; } static void set_size(int n = 3000000) { MAX = (n > 1 ? n : 1) + 1; if((int)fac.size() >= MAX) return; fac.resize(MAX); finv.resize(MAX); inv.resize(MAX); const int MOD = T::mod(); fac[0] = fac[1] = 1; finv[0] = finv[1] = 1; inv[1] = 1; for(int i = 2; i < MAX; i++) { fac[i] = fac[i - 1] * i; inv[i] = (T)MOD - inv[MOD % i] * (MOD / i); finv[i] = finv[i - 1] * inv[i]; } } }; template <class T> int factorial<T>::MAX = 0; template <class T> std::vector<T> factorial<T>::fac; template <class T> std::vector<T> factorial<T>::finv; template <class T> std::vector<T> factorial<T>::inv; #line 9 "/Users/nok0/Documents/Programming/nok0/math/formal_power_series.hpp" enum Mode { FAST = 1, NAIVE = -1, }; template <class T, Mode mode = FAST> struct formal_power_series : std::vector<T> { factorial<T> fact; using std::vector<T>::vector; using std::vector<T>::size; using std::vector<T>::resize; using std::vector<T>::begin; using std::vector<T>::insert; using std::vector<T>::erase; using F = formal_power_series; using S = std::vector<std::pair<int, T>>; F &operator+=(const F &g) { for(int i = 0; i < int(std::min((*this).size(), g.size())); i++) (*this)[i] += g[i]; return *this; } F &operator+=(const T &t) { assert(int((*this).size())); (*this)[0] += t; return *this; } F &operator-=(const F &g) { for(int i = 0; i < int(std::min((*this).size(), g.size())); i++) (*this)[i] -= g[i]; return *this; } F &operator-=(const T &t) { assert(int((*this).size())); (*this)[0] -= t; return *this; } F &operator*=(const T &t) { for(int i = 0; i < int((*this).size()); ++i) (*this)[i] *= t; return *this; } F &operator/=(const T &t) { T div = t.inv(); for(int i = 0; i < int((*this).size()); ++i) (*this)[i] *= div; return *this; } F &operator>>=(const int sz) { assert(sz >= 0); int n = (*this).size(); (*this).erase((*this).begin(), (*this).begin() + std::min(sz, n)); (*this).resize(n); return *this; } F &operator<<=(const int sz) { assert(sz >= 0); int n = (*this).size(); (*this).insert((*this).begin(), sz, T(0)); (*this).resize(n); return *this; } F poly_div(const F &g) { if(this->size() < g.size()) { F ret(this->size()); return ret; } if(mode == FAST) { auto ret = *this; int old = this->size(); int n = old - g.size() + 1; ret = ((*this).rev().pre(n) * g.rev().inv(n)); ret.rev_inplace(); ret.resize(old); return ret; } else { assert(g.back() != T(0)); T igb = g.back().inv(); int n = (*this).size(), m = g.size(); F this_copy(*this); F ret(n); for(int i = n - 1; i >= m - 1; --i) { T mul = this_copy[i] * igb; ret[i - m + 1] = mul; for(int j = i; j > i - m; j--) this_copy[j] -= g[j - i + m - 1] * mul; } return ret; } } //これのみ多項式の除算として扱う F &operator%=(const F &g) { return *this -= this->poly_div(g) * g; } F &operator=(const std::vector<T> &v) { int n = (*this).size(); for(int i = 0; i < n; ++i) (*this)[i] = v[i]; return *this; } F operator-() const { F ret = *this; return ret * -1; } F &operator*=(const F &g) { if(mode == FAST) { int n = (*this).size(); auto tmp = atcoder::convolution(*this, g); for(int i = 0; i < n; ++i) (*this)[i] = tmp[i]; return *this; } else { int n = (*this).size(), m = g.size(); for(int i = n - 1; i >= 0; --i) { (*this)[i] *= g[0]; for(int j = 1; j < std::min(i + 1, m); j++) (*this)[i] += (*this)[i - j] * g[j]; } return *this; } } F &operator/=(const F &g) { if((*this).size() < g.size()) { (*this).assign((*this).size(), T(0)); return *this; } if(mode == FAST) { *this *= g.inv(); return *this; } else { assert(g[0] != T(0)); T ig0 = g[0].inv(); int n = (*this).size(), m = g.size(); for(int i = 0; i < n; ++i) { for(int j = 1; j < std::min(i + 1, m); ++j) (*this)[i] -= (*this)[i - j] * g[j]; (*this)[i] *= ig0; } return *this; } } F &operator*=(S g) { int n = (*this).size(); auto [d, c] = g.front(); if(!d) g.erase(g.begin()); else c = 0; for(int i = n - 1; i >= 0; --i) { (*this)[i] *= c; for(auto &[j, b] : g) { if(j > i) break; (*this)[i] += (*this)[i - j] * b; } } return *this; } F &operator/=(S g) { int n = (*this).size(); auto [d, c] = g.front(); assert(!d and c != 0); T ic = c.inv(); g.erase(g.begin()); for(int i = 0; i < n; ++i) { for(auto &[j, b] : g) { if(j > i) break; (*this)[i] -= (*this)[i - j] * b; } (*this)[i] *= ic; } return *this; } F operator+(const F &g) const { return F(*this) += g; } F operator+(const T &t) const { return F(*this) += t; } F operator-(const F &g) const { return F(*this) -= g; } F operator-(const T &t) const { return F(*this) -= t; } F operator*(const F &g) const { return F(*this) *= g; } F operator*(const T &t) const { return F(*this) *= t; } F operator/(const F &g) const { return F(*this) /= g; } F operator/(const T &t) const { return F(*this) /= t; } F operator%(const F &g) const { return F(*this) %= g; } F operator*=(const S &g) const { return F(*this) *= g; } F operator/=(const S &g) const { return F(*this) /= g; } F pre(int d) const { return F((*this).begin(), (*this).begin() + std::min((int)(*this).size(), d)); } F &shrink() { while((int)(*this).size() > 1 and (*this).back() == T(0)) (*this).pop_back(); return *this; } F &rev_inplace() { reverse((*this).begin(), (*this).end()); return *this; } F rev() const { return F(*this).rev_inplace(); } // *=(1 + cz^d) F &multiply(const int d, const T c) { int n = (*this).size(); if(c == T(1)) for(int i = n - d - 1; i >= 0; --i) (*this)[i + d] += (*this)[i]; else if(c == T(-1)) for(int i = n - d - 1; i >= 0; --i) (*this)[i + d] -= (*this)[i]; else for(int i = n - d - 1; i >= 0; --i) (*this)[i + d] += (*this)[i] * c; return *this; } // /=(1 + cz^d) F &divide(const int d, const T c) { int n = (*this).size(); if(c == T(1)) for(int i = 0; i < n - d; ++i) (*this)[i + d] -= (*this)[i]; else if(c == T(-1)) for(int i = 0; i < n - d; ++i) (*this)[i + d] += (*this)[i]; else for(int i = 0; i < n - d; ++i) (*this)[i + d] -= (*this)[i] * c; return *this; } //Ο(N) T eval(const T &t) const { int n = (*this).size(); T res = 0, tmp = 1; for(int i = 0; i < n; ++i) res += (*this)[i] * tmp, tmp *= t; return res; } F inv(int deg = -1) const { int n = (*this).size(); assert(mode == FAST and n and (*this)[0] != 0); if(deg == -1) deg = n; assert(deg > 0); F res{(*this)[0].inv()}; while(int(res.size()) < deg) { int m = res.size(); F f((*this).begin(), (*this).begin() + std::min(n, m * 2)), r(res); f.resize(m * 2), atcoder::internal::butterfly(f); r.resize(m * 2), atcoder::internal::butterfly(r); for(int i = 0; i < m * 2; ++i) f[i] *= r[i]; atcoder::internal::butterfly_inv(f); f.erase(f.begin(), f.begin() + m); f.resize(m * 2), atcoder::internal::butterfly(f); for(int i = 0; i < m * 2; ++i) f[i] *= r[i]; atcoder::internal::butterfly_inv(f); T iz = T(m * 2).inv(); iz *= -iz; for(int i = 0; i < m; ++i) f[i] *= iz; res.insert(res.end(), f.begin(), f.begin() + m); } res.resize(deg); return res; } //Ο(N) F &diff_inplace() { int n = (*this).size(); for(int i = 1; i < n; ++i) (*this)[i - 1] = (*this)[i] * i; (*this)[n - 1] = 0; return *this; } F diff() const { F(*this).diff_inplace(); } //Ο(N) F &integral_inplace() { int n = (*this).size(), mod = T::mod(); std::vector<T> inv(n); { inv[1] = 1; for(int i = 2; i < n; ++i) inv[i] = T(mod) - inv[mod % i] * (mod / i); } for(int i = n - 2; i >= 0; --i) (*this)[i + 1] = (*this)[i] * inv[i + 1]; (*this)[0] = 0; return *this; } F integral() const { return F(*this).integral_inplace(); } //Ο(NlogN) F &log_inplace() { int n = (*this).size(); assert(n and (*this)[0] == 1); F f_inv = (*this).inv(); (*this).diff_inplace(); (*this) *= f_inv; (*this).integral_inplace(); return *this; } F log() const { return F(*this).log_inplace(); } //Ο(NlogN) F &deriv_inplace() { int n = (*this).size(); assert(n); for(int i = 2; i < n; ++i) (*this)[i] *= i; (*this).erase((*this).begin()); (*this).push_back(0); return *this; } F deriv() const { return F(*this).deriv_inplace(); } //Ο(NlogN) F &exp_inplace() { int n = (*this).size(); assert(n and (*this)[0] == 0); F g{1}; (*this)[0] = 1; F h_drv((*this).deriv()); for(int m = 1; m < n; m *= 2) { F f((*this).begin(), (*this).begin() + m); f.resize(2 * m), atcoder::internal::butterfly(f); auto mult_f = [&](F &p) { p.resize(2 * m); atcoder::internal::butterfly(p); for(int i = 0; i < 2 * m; ++i) p[i] *= f[i]; atcoder::internal::butterfly_inv(p); p /= 2 * m; }; if(m > 1) { F g_(g); g_.resize(2 * m), atcoder::internal::butterfly(g_); for(int i = 0; i < 2 * m; ++i) g_[i] *= g_[i] * f[i]; atcoder::internal::butterfly_inv(g_); T iz = T(-2 * m).inv(); g_ *= iz; g.insert(g.end(), g_.begin() + m / 2, g_.begin() + m); } F t((*this).begin(), (*this).begin() + m); t.deriv_inplace(); { F r{h_drv.begin(), h_drv.begin() + m - 1}; mult_f(r); for(int i = 0; i < m; ++i) t[i] -= r[i] + r[m + i]; } t.insert(t.begin(), t.back()); t.pop_back(); t *= g; F v((*this).begin() + m, (*this).begin() + std::min(n, 2 * m)); v.resize(m); t.insert(t.begin(), m - 1, 0); t.push_back(0); t.integral_inplace(); for(int i = 0; i < m; ++i) v[i] -= t[m + i]; mult_f(v); for(int i = 0; i < std::min(n - m, m); ++i) (*this)[m + i] = v[i]; } return *this; } F exp() const { return F(*this).exp_inplace(); } //Ο(NlogN) F &pow_inplace(long long k) { int n = (*this).size(), l = 0; assert(k >= 0); if(!k) { for(int i = 0; i < n; ++i) (*this)[i] = !i; return *this; } while(l < n and (*this)[l] == 0) ++l; if(l > (n - 1) / k or l == n) return *this = F(n); T c = (*this)[l]; (*this).erase((*this).begin(), (*this).begin() + l); (*this) /= c; (*this).log_inplace(); (*this).resize(n - l * k); (*this) *= k; (*this).exp_inplace(); (*this) *= c.pow(k); (*this).insert((*this).begin(), l * k, 0); return *this; } F pow(const long long k) const { return F(*this).pow_inplace(k); } //Ο(NlogN) F sqrt(int deg = -1) const { auto SQRT = [&](T t) { int mod = T::mod(); if(t == 0 or t == 1) return t; int v = (mod - 1) / 2; if(t.pow(v) != 1) return T(-1); int q = mod - 1, m = 0; while(~q & 1) q >>= 1, m++; std::mt19937 mt; T z = mt(); while(z.pow(v) != mod - 1) z = mt(); T c = z.pow(q), u = t.pow(q), r = t.pow((q + 1) / 2); for(; m > 1; m--) { T tmp = u.pow(1 << (m - 2)); if(tmp != 1) r = r * c, u = u * c * c; c = c * c; } return T(std::min(r.val(), mod - r.val())); }; int n = (*this).size(); if(deg == -1) deg = n; if((*this)[0] == 0) { for(int i = 1; i < n; i++) { if((*this)[i] != 0) { if(i & 1) return F(0); if(deg - i / 2 <= 0) break; auto ret = (*this); ret >>= i; ret.resize(n - i); ret = ret.sqrt(deg - i / 2); if(ret.empty()) return F(0); ret <<= (i / 2); ret.resize(deg); return ret; } } return F(deg); } auto sqr = SQRT((*this)[0]); if(sqr * sqr != (*this)[0]) return F(0); F ret{sqr}; T ti = T(1) / T(2); for(int i = 1; i < deg; i <<= 1) { auto u = (*this); u.resize(i << 1); ret = (ret.inv(i << 1) * u + ret) * ti; } ret.resize(deg); return ret; } void sparse_pow(const int n, const int d, const T c, const int k) { F ret(n); T tmp = 1; if(k >= 0) { for(int i = 0; i < n; i += d) { ret[i] = fact.binom(k, i / d) * tmp; tmp *= c; } } else { for(int i = 0; i < n; i += d) { ret[i] = fact.binom(i / d - k - 1, -k - 1) * tmp; tmp *= -c; } } (*this) = ret; } void sparse_pow_inv(const int n, const int d, const T c, const int k) { return sparse_pow(n, d, c, -k); } void stirling_first(int n) { if(!n) { *this = F{1}; return; } int m = 1; F res(n + 1); res[1] = 1; for(int k = 30 - __builtin_clz(n); k >= 0; --k) { F as(m * 2 + 1), bs(m + 1); for(int i = 0; i <= m; i++) as[i] = fact.fac[i] * res[i]; bs[m] = 1; for(int i = m - 1; i >= 0; i--) bs[i] -= bs[i + 1] * m; for(int i = 0; i <= m; i++) bs[m - i] *= fact.finv[i]; F cs = as * bs, ds(m + 1); for(int i = 0; i <= m; i++) ds[i] = cs[m + i] * fact.finv[i]; res *= ds; m <<= 1; if(n >> k & 1) { F g(n + 1); for(int i = 0; i <= m; i++) { g[i] -= res[i] * m; g[i + 1] += res[i]; } res = g; m |= 1; } } *this = res; } void stirling_second(int n) { F f(n + 1), g(n + 1); for(int i = 0; i <= n; i++) { f[i] = T(i).pow(n) * fact.finv[i]; g[i] = fact.finv[i] * (i % 2 ? -1 : 1); } f *= g; *this = f; } //return f(x + c) F taylor_shift(int c) { F f(*this); int n = this->size(); for(int i = 0; i < n; i++) f[i] *= fact.fac[i]; reverse(f.begin(), f.end()); F g(n, 1); T mul = 1; for(int i = 1; i < n; i++) g[i] = (mul *= c) * fact.finv[i]; f *= g; reverse(f.begin(), f.end()); for(int i = 0; i < n; i++) f[i] *= fact.finv[i]; return f; } F taylor_shift(T c) { return taylor_shift(c.val()); } std::vector<T> multipoint_evaluation(const std::vector<T> &p); }; #line 2 "/Users/nok0/Documents/Programming/nok0/math/modint_iostream.hpp" #line 4 "/Users/nok0/Documents/Programming/nok0/math/modint_iostream.hpp" template <int m> std::istream &std::operator>>(std::istream &is, atcoder::static_modint<m> &a) { long long v; is >> v; a = v; return is; } template <int m> std::istream &std::operator>>(std::istream &is, atcoder::dynamic_modint<m> &a) { long long v; is >> v; a = v; return is; } template <int m> std::ostream &std::operator<<(std::ostream &os, const atcoder::static_modint<m> &a) { return os << a.val(); } template <int m> std::ostream &std::operator<<(std::ostream &os, const atcoder::dynamic_modint<m> &a) { return os << a.val(); } #line 7 "a.cpp" using mint = atcoder::modint998244353; using fps = formal_power_series<mint, FAST>; void main_() { factorial<mint>::set_size(); INT(n, c); fps f(n); cin >> f; fps g = f.taylor_shift(c); print(g); }