# Submit Info #8212

Problem Lang User Status Time Memory
Polynomial Taylor Shift cpp emthrm AC 530 ms 26.80 MiB

ケース詳細
Name Status Time Memory
example_00 AC 1 ms 0.71 MiB
example_01 AC 1 ms 0.68 MiB
fft_killer_00 AC 530 ms 26.72 MiB
fft_killer_01 AC 524 ms 26.80 MiB
max_random_00 AC 524 ms 26.72 MiB
max_random_01 AC 528 ms 26.80 MiB
medium_00 AC 4 ms 0.80 MiB
medium_01 AC 10 ms 1.05 MiB
medium_02 AC 9 ms 1.05 MiB
medium_all_zero_00 AC 3 ms 0.77 MiB
medium_c_zero_00 AC 4 ms 0.80 MiB
random_00 AC 504 ms 24.19 MiB
random_01 AC 511 ms 25.55 MiB
random_02 AC 58 ms 3.77 MiB
small_00 AC 1 ms 0.68 MiB
small_01 AC 2 ms 0.67 MiB
small_02 AC 1 ms 0.68 MiB
small_03 AC 1 ms 0.72 MiB
small_04 AC 1 ms 0.67 MiB
small_05 AC 0 ms 0.70 MiB
small_06 AC 1 ms 0.71 MiB
small_07 AC 1 ms 0.68 MiB
small_08 AC 3 ms 0.72 MiB
small_09 AC 3 ms 0.67 MiB
small_10 AC 1 ms 0.67 MiB
small_11 AC 2 ms 0.67 MiB
small_12 AC 4 ms 0.72 MiB
small_13 AC 2 ms 0.71 MiB
small_14 AC 2 ms 0.67 MiB
small_15 AC 5 ms 0.68 MiB

#define _USE_MATH_DEFINES #include <bits/stdc++.h> using namespace std; #define FOR(i,m,n) for(int i=(m);i<(n);++i) #define REP(i,n) FOR(i,0,n) #define ALL(v) (v).begin(),(v).end() using ll = long long; const int INF = 0x3f3f3f3f; const ll LINF = 0x3f3f3f3f3f3f3f3fLL; const double EPS = 1e-8; const int MOD = 1000000007; // const int MOD = 998244353; const int dy[] = {1, 0, -1, 0}, dx[] = {0, -1, 0, 1}; const int dy8[] = {1, 1, 0, -1, -1, -1, 0, 1}, dx8[] = {0, -1, -1, -1, 0, 1, 1, 1}; template <typename T, typename U> inline bool chmax(T &a, U b) { return a < b ? (a = b, true) : false; } template <typename T, typename U> inline bool chmin(T &a, U b) { return a > b ? (a = b, true) : false; } struct IOSetup { IOSetup() { cin.tie(nullptr); ios_base::sync_with_stdio(false); cout << fixed << setprecision(20); } } iosetup; int mod = MOD; struct ModInt { unsigned val; ModInt(): val(0) {} ModInt(ll x) : val(x >= 0 ? x % mod : x % mod + mod) {} ModInt pow(ll exponent) { ModInt tmp = *this, res = 1; while (exponent > 0) { if (exponent & 1) res *= tmp; tmp *= tmp; exponent >>= 1; } return res; } ModInt &operator+=(const ModInt &x) { if((val += x.val) >= mod) val -= mod; return *this; } ModInt &operator-=(const ModInt &x) { if((val += mod - x.val) >= mod) val -= mod; return *this; } ModInt &operator*=(const ModInt &x) { val = static_cast<unsigned long long>(val) * x.val % mod; return *this; } ModInt &operator/=(const ModInt &x) { // assert(__gcd(static_cast<int>(x.val), mod) == 1); unsigned a = x.val, b = mod; int u = 1, v = 0; while (b) { unsigned tmp = a / b; swap(a -= tmp * b, b); swap(u -= tmp * v, v); } return *this *= u; } bool operator==(const ModInt &x) const { return val == x.val; } bool operator!=(const ModInt &x) const { return val != x.val; } bool operator<(const ModInt &x) const { return val < x.val; } bool operator<=(const ModInt &x) const { return val <= x.val; } bool operator>(const ModInt &x) const { return val > x.val; } bool operator>=(const ModInt &x) const { return val >= x.val; } ModInt &operator++() { if (++val == mod) val = 0; return *this; } ModInt operator++(int) { ModInt res = *this; ++*this; return res; } ModInt &operator--() { val = (val == 0 ? mod : val) - 1; return *this; } ModInt operator--(int) { ModInt res = *this; --*this; return res; } ModInt operator+() const { return *this; } ModInt operator-() const { return ModInt(val ? mod - val : 0); } ModInt operator+(const ModInt &x) const { return ModInt(*this) += x; } ModInt operator-(const ModInt &x) const { return ModInt(*this) -= x; } ModInt operator*(const ModInt &x) const { return ModInt(*this) *= x; } ModInt operator/(const ModInt &x) const { return ModInt(*this) /= x; } friend ostream &operator<<(ostream &os, const ModInt &x) { return os << x.val; } friend istream &operator>>(istream &is, ModInt &x) { ll val; is >> val; x = ModInt(val); return is; } }; ModInt abs(const ModInt &x) { return x; } struct Combinatorics { int val; // "val!" and "mod" must be disjoint. vector<ModInt> fact, fact_inv, inv; Combinatorics(int val = 10000000) : val(val), fact(val + 1), fact_inv(val + 1), inv(val + 1) { fact[0] = 1; FOR(i, 1, val + 1) fact[i] = fact[i - 1] * i; fact_inv[val] = ModInt(1) / fact[val]; for (int i = val; i > 0; --i) fact_inv[i - 1] = fact_inv[i] * i; FOR(i, 1, val + 1) inv[i] = fact[i - 1] * fact_inv[i]; } ModInt nCk(int n, int k) { if (n < 0 || n < k || k < 0) return ModInt(0); // assert(n <= val && k <= val); return fact[n] * fact_inv[k] * fact_inv[n - k]; } ModInt nPk(int n, int k) { if (n < 0 || n < k || k < 0) return ModInt(0); // assert(n <= val); return fact[n] * fact_inv[n - k]; } ModInt nHk(int n, int k) { if (n < 0 || k < 0) return ModInt(0); return (k == 0 ? ModInt(1) : nCk(n + k - 1, k)); } }; template <typename T> function<vector<T>(const vector<T>&, const vector<T>&)> mul = [](const vector<T> &a, const vector<T> &b) { int n = a.size(), m = b.size(); vector<T> res(n + m - 1, T(0)); REP(i, n) REP(j, m) res[i + j] += a[i] * b[j]; return res; }; template <typename T> function<bool(const T&, T&)> sqr = [](const T &a, T &res) { return false; }; template <typename T> struct FPS { vector<T> co; FPS(int deg = 0) : co(deg + 1, T(0)) {} FPS(const vector<T> &co) : co(co) {} FPS(initializer_list<T> init) : co(init.begin(), init.end()) {} template <typename InputIter> FPS(InputIter first, InputIter last) : co(first, last) {} inline const T &operator[](int term) const { return co[term]; } inline T &operator[](int term) { return co[term]; } void resize(int deg) { int prev = co.size(); co.resize(deg + 1); if (prev < deg + 1) fill(co.begin() + prev, co.end(), T(0)); } void shrink() { while (co.size() > 1 && co.back() == T(0)) co.pop_back(); } int degree() const { return static_cast<int>(co.size()) - 1; } FPS &operator=(const vector<T> &new_co) { co.resize(new_co.size()); copy(ALL(new_co), co.begin()); return *this; } FPS &operator=(const FPS &x) { co.resize(x.co.size()); copy(ALL(x.co), co.begin()); return *this; } FPS &operator+=(const FPS &x) { int n = x.co.size(); if (n > co.size()) resize(n - 1); REP(i, n) co[i] += x.co[i]; return *this; } FPS &operator-=(const FPS &x) { int n = x.co.size(); if (n > co.size()) resize(n - 1); REP(i, n) co[i] -= x.co[i]; return *this; } FPS &operator*=(T x) { for (T &e : co) e *= x; return *this; } FPS &operator*=(const FPS &x) { return *this = mul<T>(co, x.co); } FPS &operator/=(T x) { assert(x != T(0)); T inv_x = T(1) / x; for (T &e : co) e *= inv_x; return *this; } FPS &operator/=(const FPS &x) { if (x.co.size() > co.size()) return *this = FPS(); int n = co.size() - x.co.size() + 1; FPS a(co.rbegin(), co.rbegin() + n), b(x.co.rbegin(), x.co.rbegin() + min(static_cast<int>(x.co.size()), n)); b = b.inv(n - 1); a *= b; return *this = FPS(a.co.rend() - n, a.co.rend()); } FPS &operator%=(const FPS &x) { *this -= *this / x * x; co.resize(static_cast<int>(x.co.size()) - 1); if (co.empty()) co = {T(0)}; return *this; } FPS &operator<<=(int n) { co.insert(co.begin(), n, T(0)); return *this; } FPS &operator>>=(int n) { if (co.size() < n) return *this = FPS(); co.erase(co.begin(), co.begin() + n); return *this; } bool operator==(const FPS &x) const { FPS a(*this), b(x); a.shrink(); b.shrink(); int n = a.co.size(); if (n != b.co.size()) return false; REP(i, n) if (a.co[i] != b.co[i]) return false; return true; } bool operator!=(const FPS &x) const { return !(*this == x); } FPS operator+() const { return *this; } FPS operator-() const { FPS res(*this); for (T &e : res.co) e = T(-e); return res; } FPS operator+(const FPS &x) const { return FPS(*this) += x; } FPS operator-(const FPS &x) const { return FPS(*this) -= x; } FPS operator*(T x) const { return FPS(*this) *= x; } FPS operator*(const FPS &x) const { return FPS(*this) *= x; } FPS operator/(T x) const { return FPS(*this) /= x; } FPS operator/(const FPS &x) const { return FPS(*this) /= x; } FPS operator%(const FPS &x) const { return FPS(*this) %= x; } FPS operator<<(int n) const { return FPS(*this) <<= n; } FPS operator>>(int n) const { return FPS(*this) >>= n; } T horner(T val) const { T res = T(0); for (int i = static_cast<int>(co.size()) - 1; i >= 0; --i) (res *= val) += co[i]; return res; } FPS differential() const { int n = co.size(); assert(n >= 1); FPS res(n - 1); FOR(i, 1, n) res.co[i - 1] = co[i] * T(i); return res; } FPS integral() const { int n = co.size(); FPS res(n + 1); REP(i, n) res[i + 1] = co[i] / T(i + 1); return res; } FPS exp(int deg = -1) const { assert(co[0] == T(0)); if (deg == -1) deg = static_cast<int>(co.size()) - 1; FPS one({T(1)}), res = one; for (int i = 1; i <= deg; i <<= 1) { res *= FPS(co.begin(), co.begin() + min(static_cast<int>(co.size()), i << 1)) - res.log((i << 1) - 1) + one; res.co.resize(i << 1); } res.co.resize(deg + 1); return res; } FPS inv(int deg = -1) const { assert(co[0] != T(0)); if (deg == -1) deg = static_cast<int>(co.size()) - 1; FPS res({T(1) / co[0]}); for (int i = 1; i <= deg; i <<= 1) { res = res + res - res * res * FPS(co.begin(), co.begin() + min(static_cast<int>(co.size()), i << 1)); res.co.resize(i << 1); } res.co.resize(deg + 1); return res; } FPS log(int deg = -1) const { assert(co[0] == T(1)); if (deg == -1) deg = static_cast<int>(co.size()) - 1; FPS integrand = differential() * inv(deg - 1); integrand.co.resize(deg); return integrand.integral(); } FPS pow(ll exponent, int deg = -1) const { int n = co.size(); if (deg == -1) deg = n - 1; REP(i, n) { if (co[i] != T(0)) { ll shift = exponent * i; if (shift > deg) break; T tmp = 1, base = co[i]; ll e = exponent; while (e > 0) { if (e & 1) tmp *= base; base *= base; e >>= 1; } return ((((*this >> i) * (T(1) / co[i])).log(deg - shift) * T(exponent)).exp(deg - shift) * tmp) << shift; } } return FPS(deg); } FPS mod_pow(ll exponent, const FPS &md) const { FPS inv_rev_md = FPS(md.co.rbegin(), md.co.rend()).inv(); int deg_of_md = md.co.size(); function<void(FPS&, const FPS&)> mod_mul = [&](FPS &multiplicand, const FPS &multiplier) { multiplicand *= multiplier; if (deg_of_md <= multiplicand.co.size()) { int n = multiplicand.co.size() - deg_of_md + 1; FPS quotient = FPS(multiplicand.co.rbegin(), multiplicand.co.rbegin() + n) * FPS(inv_rev_md.co.begin(), inv_rev_md.co.begin() + min(static_cast<int>(inv_rev_md.co.size()), n)); multiplicand -= FPS(quotient.co.rend() - n, quotient.co.rend()) * md; } multiplicand.co.resize(deg_of_md - 1); if (multiplicand.co.empty()) multiplicand.co = {T(0)}; }; FPS res({T(1)}), base = *this; mod_mul(base, res); while (exponent > 0) { if (exponent & 1) mod_mul(res, base); mod_mul(base, base); exponent >>= 1; } return res; } FPS sqrt(int deg = -1) const { int n = co.size(); if (deg == -1) deg = n - 1; if (co[0] == T(0)) { FOR(i, 1, n) { if (co[i] == T(0)) continue; if (i & 1) return FPS(-1); int shift = i >> 1; if (deg < shift) break; FPS res = (*this >> i).sqrt(deg - shift); if (res.co.empty()) return FPS(-1); res <<= shift; res.resize(deg); return res; } return FPS(deg); } T s; if (!sqr<T>(co[0], s)) return FPS(-1); FPS res({s}); T half = T(1) / T(2); for (int i = 1; i <= deg; i <<= 1) { (res += FPS(co.begin(), co.begin() + min(static_cast<int>(co.size()), i << 1)) * res.inv((i << 1) - 1)) *= half; } res.resize(deg); return res; } FPS translate(T c) const { int n = co.size(); vector<T> fact(n, T(1)), inv_fact(n, T(1)); FOR(i, 1, n) fact[i] = fact[i - 1] * T(i); inv_fact[n - 1] = T(1) / fact[n - 1]; for (int i = n - 1; i > 0; --i) inv_fact[i - 1] = inv_fact[i] * T(i); vector<T> g(n), ex(n); REP(i, n) g[n - 1 - i] = co[i] * fact[i]; T pow_c = T(1); REP(i, n) { ex[i] = pow_c * inv_fact[i]; pow_c *= c; } vector<T> conv = mul<T>(g, ex); FPS res(n - 1); REP(i, n) res[i] = conv[n - 1 - i] * inv_fact[i]; return res; } }; struct NTT { NTT(int mod_) { for (int i = 0; ; ++i) { assert(i < 23); if (primes[i][0] == mod_) { mod = mod_; n_max = 1 << primes[i][2]; root = ModInt(primes[i][1]).pow((mod - 1) >> primes[i][2]); break; } } } void sub_dft(vector<ModInt> &a) { int n = a.size(); // assert(__builtin_popcount(n) == 1); calc(n); int shift = __builtin_ctz(butterfly.size()) - __builtin_ctz(n); REP(i, n) { int j = butterfly[i] >> shift; if (i < j) swap(a[i], a[j]); } for (int block = 1; block < n; block <<= 1) { int den = __builtin_ctz(block); for (int i = 0; i < n; i += (block << 1)) REP(j, block) { ModInt tmp = a[i + j + block] * omega[den][j]; a[i + j + block] = a[i + j] - tmp; a[i + j] += tmp; } } } template <typename T> vector<ModInt> dft(const vector<T> &a) { int n = a.size(), lg = 1; while ((1 << lg) < n) ++lg; vector<ModInt> A(1 << lg, 0); REP(i, n) A[i] = a[i]; sub_dft(A); return A; } void idft(vector<ModInt> &a) { int n = a.size(); // assert(__builtin_popcount(n) == 1); sub_dft(a); reverse(a.begin() + 1, a.end()); ModInt inv_n = ModInt(1) / n; REP(i, n) a[i] *= inv_n; } template <typename T> vector<ModInt> convolution(const vector<T> &a, const vector<T> &b) { int a_sz = a.size(), b_sz = b.size(), sz = a_sz + b_sz - 1, lg = 1; while ((1 << lg) < sz) ++lg; int n = 1 << lg; vector<ModInt> A(n, 0), B(n, 0); REP(i, a_sz) A[i] = a[i]; REP(i, b_sz) B[i] = b[i]; sub_dft(A); sub_dft(B); REP(i, n) A[i] *= B[i]; idft(A); A.resize(sz); return A; } private: const int primes[23][3] = { {16957441, 329, 14}, {17006593, 26, 15}, {19529729, 770, 17}, {167772161, 3, 25}, {469762049, 3, 26}, {645922817, 3, 23}, {897581057, 3, 23}, {924844033, 5, 21}, {935329793, 3, 22}, {943718401, 7, 22}, {950009857, 7, 21}, {962592769, 7, 21}, {975175681, 17, 21}, {976224257, 3, 20}, {985661441, 3, 22}, {998244353, 3, 23}, {1004535809, 3, 21}, {1007681537, 3, 20}, {1012924417, 5, 21}, {1045430273, 3, 20}, {1051721729, 6, 20}, {1053818881, 7, 20}, {1224736769, 3, 24} }; int n_max; ModInt root; vector<int> butterfly{0}; vector<vector<ModInt>> omega{{1}}; void calc(int n) { int prev_n = butterfly.size(); if (n <= prev_n) return; // assert(n <= n_max); butterfly.resize(n); int prev_lg = omega.size(), lg = __builtin_ctz(n); FOR(i, 1, prev_n) butterfly[i] <<= lg - prev_lg; FOR(i, prev_n, n) butterfly[i] = (butterfly[i >> 1] >> 1) | ((i & 1) << (lg - 1)); omega.resize(lg); FOR(i, prev_lg, lg) { omega[i].resize(1 << i); ModInt tmp = root.pow((mod - 1) / (1 << (i + 1))); REP(j, 1 << (i - 1)) { omega[i][j << 1] = omega[i - 1][j]; omega[i][(j << 1) + 1] = omega[i - 1][j] * tmp; } } } }; int main() { NTT ntt(998244353); mul<ModInt> = [&](const vector<ModInt> &a, const vector<ModInt> &b) { return ntt.convolution(a, b); }; int n, c; cin >> n >> c; FPS<ModInt> fps(n - 1); REP(i, n) cin >> fps[i]; fps = fps.translate(c); REP(i, n) cout << fps[i] << " \n"[i + 1 == n]; return 0; }