# Submit Info #12240

Problem Lang User Status Time Memory
Polynomial Taylor Shift cpp koosaga AC 637 ms 42.86 MiB

ケース詳細
Name Status Time Memory
example_00 AC 6 ms 8.80 MiB
example_01 AC 6 ms 8.77 MiB
fft_killer_00 AC 627 ms 42.77 MiB
fft_killer_01 AC 635 ms 42.86 MiB
max_random_00 AC 637 ms 42.86 MiB
max_random_01 AC 617 ms 42.77 MiB
medium_00 AC 7 ms 8.80 MiB
medium_01 AC 12 ms 9.05 MiB
medium_02 AC 11 ms 8.99 MiB
medium_all_zero_00 AC 9 ms 8.82 MiB
medium_c_zero_00 AC 6 ms 8.80 MiB
random_00 AC 334 ms 27.19 MiB
random_01 AC 379 ms 28.07 MiB
random_02 AC 41 ms 11.05 MiB
small_00 AC 6 ms 8.79 MiB
small_01 AC 8 ms 8.80 MiB
small_02 AC 7 ms 8.70 MiB
small_03 AC 8 ms 8.76 MiB
small_04 AC 6 ms 8.80 MiB
small_05 AC 8 ms 8.79 MiB
small_06 AC 6 ms 8.73 MiB
small_07 AC 6 ms 8.79 MiB
small_08 AC 9 ms 8.69 MiB
small_09 AC 7 ms 8.80 MiB
small_10 AC 5 ms 8.78 MiB
small_11 AC 2 ms 8.79 MiB
small_12 AC 7 ms 8.77 MiB
small_13 AC 8 ms 8.79 MiB
small_14 AC 8 ms 8.78 MiB
small_15 AC 6 ms 8.80 MiB

#include <bits/stdc++.h> #define sz(v) ((int)(v).size()) #define all(v) (v).begin(), (v).end() using namespace std; using lint = long long; const int mod = 998244353; //1e9 + 7;//998244353; const int MAXN = 530000; template<typename T> T gcd(const T &a, const T &b) { return b == T(0) ? a : gcd(b, a % b); } struct mint { int val; mint() { val = 0; } mint(const lint &v) { val = (-mod <= v && v < mod) ? v : v % mod; if (val < 0) val += mod; } friend ostream &operator<<(ostream &os, const mint &a) { return os << a.val; } friend bool operator==(const mint &a, const mint &b) { return a.val == b.val; } friend bool operator!=(const mint &a, const mint &b) { return !(a == b); } friend bool operator<(const mint &a, const mint &b) { return a.val < b.val; } mint operator-() const { return mint(-val); } mint &operator+=(const mint &m) { if ((val += m.val) >= mod) val -= mod; return *this; } mint &operator-=(const mint &m) { if ((val -= m.val) < 0) val += mod; return *this; } mint &operator*=(const mint &m) { val = (lint) val * m.val % mod; return *this; } friend mint ipow(mint a, lint p) { mint ans = 1; for (; p; p /= 2, a *= a) if (p & 1) ans *= a; return ans; } friend mint inv(const mint &a) { assert(a.val); return ipow(a, mod - 2); } mint &operator/=(const mint &m) { return (*this) *= inv(m); } friend mint operator+(mint a, const mint &b) { return a += b; } friend mint operator-(mint a, const mint &b) { return a -= b; } friend mint operator*(mint a, const mint &b) { return a *= b; } friend mint operator/(mint a, const mint &b) { return a /= b; } operator int64_t() const { return val; } }; namespace fft { using real_t = double; using base = complex<real_t>; void fft(vector<base> &a, bool inv) { int n = a.size(), j = 0; vector<base> roots(n / 2); for (int i = 1; i < n; i++) { int bit = (n >> 1); while (j >= bit) { j -= bit; bit >>= 1; } j += bit; if (i < j) swap(a[i], a[j]); } real_t ang = 2 * acos(real_t(-1)) / n * (inv ? -1 : 1); for (int i = 0; i < n / 2; i++) { roots[i] = base(cos(ang * i), sin(ang * i)); } /* XOR Convolution : set roots[*] = 1. OR Convolution : set roots[*] = 1, and do following: if (!inv) { a[j + k] = u + v; a[j + k + i/2] = u; } else { a[j + k] = v; a[j + k + i/2] = u - v; } */ for (int i = 2; i <= n; i <<= 1) { int step = n / i; for (int j = 0; j < n; j += i) { for (int k = 0; k < i / 2; k++) { base u = a[j + k], v = a[j + k + i / 2] * roots[step * k]; a[j + k] = u + v; a[j + k + i / 2] = u - v; } } } if (inv) for (int i = 0; i < n; i++) a[i] /= n; // skip for OR convolution. } template<typename T> void ntt(vector<T> &a, bool inv) { const int prr = 3; // primitive root int n = a.size(), j = 0; vector<T> roots(n / 2); for (int i = 1; i < n; i++) { int bit = (n >> 1); while (j >= bit) { j -= bit; bit >>= 1; } j += bit; if (i < j) swap(a[i], a[j]); } T ang = ipow(T(prr), (mod - 1) / n); if (inv) ang = T(1) / ang; for (int i = 0; i < n / 2; i++) { roots[i] = (i ? (roots[i - 1] * ang) : T(1)); } for (int i = 2; i <= n; i <<= 1) { int step = n / i; for (int j = 0; j < n; j += i) { for (int k = 0; k < i / 2; k++) { T u = a[j + k], v = a[j + k + i / 2] * roots[step * k]; a[j + k] = u + v; a[j + k + i / 2] = u - v; } } } if (inv) { T rev = T(1) / T(n); for (int i = 0; i < n; i++) a[i] *= rev; } } template<typename T> vector<T> multiply_ntt(vector<T> &v, const vector<T> &w) { vector<T> fv(all(v)), fw(all(w)); int n = 2; while (n < sz(v) + sz(w)) n <<= 1; fv.resize(n); fw.resize(n); ntt(fv, 0); ntt(fw, 0); for (int i = 0; i < n; i++) fv[i] *= fw[i]; ntt(fv, 1); vector<T> ret(n); for (int i = 0; i < n; i++) ret[i] = fv[i]; return ret; } template<typename T> vector<T> multiply(vector<T> &v, const vector<T> &w) { vector<base> fv(all(v)), fw(all(w)); int n = 2; while (n < sz(v) + sz(w)) n <<= 1; fv.resize(n); fw.resize(n); fft(fv, 0); fft(fw, 0); for (int i = 0; i < n; i++) fv[i] *= fw[i]; fft(fv, 1); vector<T> ret(n); for (int i = 0; i < n; i++) ret[i] = (T) llround(fv[i].real()); return ret; } template<typename T> vector<T> multiply_mod(vector<T> v, const vector<T> &w) { int n = 2; while (n < sz(v) + sz(w)) n <<= 1; vector<base> v1(n), v2(n), r1(n), r2(n); for (int i = 0; i < v.size(); i++) { v1[i] = base(v[i] >> 15, v[i] & 32767); } for (int i = 0; i < w.size(); i++) { v2[i] = base(w[i] >> 15, w[i] & 32767); } fft(v1, 0); fft(v2, 0); for (int i = 0; i < n; i++) { int j = (i ? (n - i) : i); base ans1 = (v1[i] + conj(v1[j])) * base(0.5, 0); base ans2 = (v1[i] - conj(v1[j])) * base(0, -0.5); base ans3 = (v2[i] + conj(v2[j])) * base(0.5, 0); base ans4 = (v2[i] - conj(v2[j])) * base(0, -0.5); r1[i] = (ans1 * ans3) + (ans1 * ans4) * base(0, 1); r2[i] = (ans2 * ans3) + (ans2 * ans4) * base(0, 1); } fft(r1, 1); fft(r2, 1); vector<T> ret(n); for (int i = 0; i < n; i++) { T av = llround(r1[i].real()); T bv = llround(r1[i].imag()) + llround(r2[i].real()); T cv = llround(r2[i].imag()); av = av << 30; bv = bv << 15; ret[i] = av + bv + cv; } return ret; } template<typename T> vector<T> multiply_naive(vector<T> v, const vector<T> &w) { if (sz(v) == 0 || sz(w) == 0) return vector<T>(); vector<T> ret(sz(v) + sz(w) - 1); for (int i = 0; i < sz(v); i++) { for (int j = 0; j < sz(w); j++) { ret[i + j] += v[i] * w[j]; } } return ret; } } template<typename T> struct poly { vector<T> a; void normalize() { // get rid of leading zeroes while (!a.empty() && a.back() == T(0)) { a.pop_back(); } } poly() {} poly(T a0) { a = {a0}; normalize(); } poly(vector<T> t) : a(t) { normalize(); } int deg() const { return sz(a) - 1; } // -1 if empty T lead() const { return sz(a) ? a.back() : T(0); } T operator[](int idx) const { return idx >= (int) a.size() || idx < 0 ? T(0) : a[idx]; } T &coef(size_t idx) { // mutable reference at coefficient return a[idx]; } poly reversed() const { vector<T> b = a; reverse(all(b)); return poly(b); } poly trim(int n) const { n = min(n, sz(a)); vector<T> b(a.begin(), a.begin() + n); return poly(b); } poly operator*=(const T &x) { for (auto &it: a) { it *= x; } normalize(); return *this; } poly operator/=(const T &x) { return *this *= (T(1) / T(x)); } poly operator*(const T &x) const { return poly(*this) *= x; } poly operator/(const T &x) const { return poly(*this) /= x; } poly operator+=(const poly &p) { a.resize(max(sz(a), sz(p.a))); for (int i = 0; i < sz(p.a); i++) { a[i] += p.a[i]; } normalize(); return *this; } poly operator-=(const poly &p) { a.resize(max(sz(a), sz(p.a))); for (int i = 0; i < sz(p.a); i++) { a[i] -= p.a[i]; } normalize(); return *this; } poly operator*=(const poly &p) { *this = poly(fft::multiply_ntt(a, p.a)); normalize(); return *this; } poly inv(int n) { poly q(T(1) / a[0]); for (int i = 1; i < n; i <<= 1) { poly p = poly(2) - q * trim(i * 2); q = (p * q).trim(i * 2); } return q.trim(n); } pair<poly, poly> divmod_slow(const poly &b) const { // when divisor or quotient is small vector<T> A(a); vector<T> res; while (A.size() >= b.a.size()) { res.push_back(A.back() / b.a.back()); if (res.back() != T(0)) { for (size_t i = 0; i < b.a.size(); i++) { A[A.size() - i - 1] -= res.back() * b.a[b.a.size() - i - 1]; } } A.pop_back(); } reverse(all(res)); return {res, A}; } poly operator/=(const poly &b) { if (deg() < b.deg()) return *this = poly(); if (min(deg(), b.deg()) < 256) return *this = divmod_slow(b).first; int k = deg() - b.deg() + 1; poly ra = reversed().trim(k); poly rb = b.reversed().trim(k).inv(k); *this = (ra * rb).trim(k); while (sz(a) < k) a.push_back(T(0)); reverse(all(a)); normalize(); return *this; } poly operator%=(const poly &b) { if (deg() < b.deg()) return *this; if (min(deg(), b.deg()) < 256) return *this = divmod_slow(b).second; poly foo = poly(a); foo /= b; foo *= b; *this = poly(*this) -= foo; normalize(); return *this; } poly operator+(const poly &p) const { return poly(*this) += p; } poly operator-(const poly &p) const { return poly(*this) -= p; } poly operator*(const poly &p) const { return poly(*this) *= p; } poly operator/(const poly &p) const { return poly(*this) /= p; } poly operator%(const poly &p) const { return poly(*this) %= p; } poly deriv() { // calculate derivative vector<T> res; for (int i = 1; i <= deg(); i++) { res.push_back(T(i) * a[i]); } return res; } poly integr() { // calculate integral with C = 0 vector<T> res = {0}; for (int i = 0; i <= deg(); i++) { res.push_back(a[i] / T(i + 1)); } return res; } poly ln(int n) { assert(sz(a) > 0 && a[0] == T(1)); return (deriv() * inv(n)).integr().trim(n); } poly exp(int n) { if (sz(a) == 0) { return poly({T(1)}); } assert(sz(a) > 0 && a[0] == T(0)); poly q(1); for (int i = 1; i < n; i <<= 1) { poly p = poly(1) + trim(2 * i) - q.ln(2 * i); q = (q * p).trim(2 * i); } return q.trim(n); } poly power(int n, int k) { if (sz(a) == 0) return poly(); if (k == 0) return poly(T(1)).trim(n); if (k == 1) return trim(n); int ptr = 0; while (ptr < sz(a) && a[ptr] == T(0)) ptr++; if (1ll * ptr * k >= n) return poly(); n -= ptr * k; poly p(vector<T>(a.begin() + ptr, a.end())); T coeff = a[ptr]; p /= coeff; p = p.ln(n); p *= k; p = p.exp(n); p *= ipow(coeff, k); vector<T> q(ptr * k, T(0)); for (int i = 0; i <= p.deg(); i++) q.push_back(p[i]); return poly(q); } poly root(int n, int k = 2) { // NOT TESTED in K > 2 assert(sz(a) > 0 && a[0] == T(1) && k >= 2); poly q(1); for (int i = 1; i < n; i <<= 1) { if (k == 2) q += trim(2 * i) * q.inv(2 * i); else q = q * T(k - 1) + trim(2 * i) * q.inv(2 * i).power(2 * i, k - 1); q = q.trim(2 * i) / T(k); } return q.trim(n); } }; using pol = poly<mint>; mint resultant(pol &a, pol &b) { if (a.deg() == -1 || b.deg() == -1) return 0; if (a.deg() == 0 || b.deg() == 0) { return ipow(a.lead(), b.deg()) * ipow(b.lead(), a.deg()); } if (b.deg() > a.deg()) { mint flag = (a.deg() % 2 && b.deg() % 2) ? -1 : 1; return resultant(b, a) * flag; } poly nxt = a % b; return ipow(b.lead(), a.deg() - nxt.deg()) * resultant(nxt, b); } mint fact[MAXN], pwr[MAXN]; mint a[MAXN], b[MAXN]; int main() { int n, m; scanf("%d %d", &n, &m); fact[0] = pwr[0] = mint(1); for (int i = 1; i <= n; i++) { fact[i] = fact[i - 1] * mint(i); pwr[i] = pwr[i - 1] * mint(m); } for (int i = 0; i < n; i++) { int x; scanf("%d", &x); a[i] = mint(x) * fact[i]; } for(int i=0; i<=n; i++){ b[n-i] = pwr[i] / fact[i]; } auto x = pol(vector<mint>(a, a + n + 1)); auto y = pol(vector<mint>(b, b + n + 1)); auto z = x * y; for(int i=0; i<n; i++){ printf("%lld ", z[i+n] / fact[i]); } }