Submit Info #3592

Problem Lang User Status Time Memory
Convolution (mod 1,000,000,007) cpp emthrm WA 925 ms 108.92 MiB

ケース詳細
Name Status Time Memory
example_00 AC 2 ms 0.67 MiB
example_01 AC 2 ms 0.65 MiB
fft_killer_00 WA 911 ms 108.92 MiB
fft_killer_01 WA 900 ms 108.86 MiB
max_ans_zero_00 AC 925 ms 108.92 MiB
max_random_00 AC 904 ms 108.92 MiB
max_random_01 AC 915 ms 108.92 MiB
medium_00 AC 14 ms 2.34 MiB
medium_01 AC 10 ms 1.49 MiB
medium_02 AC 8 ms 2.30 MiB
medium_all_zero_00 AC 13 ms 2.30 MiB
random_00 AC 854 ms 107.02 MiB
random_01 AC 867 ms 107.55 MiB
random_02 AC 409 ms 54.17 MiB
small_00 AC 1 ms 0.67 MiB
small_01 AC 3 ms 0.67 MiB
small_02 AC 0 ms 0.68 MiB
small_03 AC 2 ms 0.66 MiB
small_04 AC 2 ms 0.72 MiB
small_05 AC 2 ms 0.68 MiB
small_06 AC 0 ms 0.64 MiB
small_07 AC 0 ms 0.67 MiB
small_08 AC 2 ms 0.68 MiB
small_09 AC 2 ms 0.68 MiB
small_10 AC 2 ms 0.68 MiB
small_11 AC 2 ms 0.68 MiB
small_12 AC 2 ms 0.72 MiB
small_13 AC 2 ms 0.67 MiB
small_14 AC 0 ms 0.67 MiB
small_15 AC 1 ms 0.72 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; template <typename T> using posteriority_queue = priority_queue<T, vector<T>, greater<T> >; 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; } template <typename T> void unique(vector<T> &a) { a.erase(unique(ALL(a)), a.end()); } 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)); } }; namespace FFT { using Real = long double; struct Complex { Real re, im; Complex(Real re = 0, Real im = 0) : re(re), im(im) {} inline Complex operator+(const Complex &x) const { return Complex(re + x.re, im + x.im); } inline Complex operator-(const Complex &x) const { return Complex(re - x.re, im - x.im); } inline Complex operator*(const Complex &x) const { return Complex(re * x.re - im * x.im, re * x.im + im * x.re); } inline Complex mul_real(Real r) const { return Complex(re * r, im * r); } inline Complex mul_pin(Real r) const { return Complex(-im * r, re * r); } inline Complex conj() const { return Complex(re, -im); } }; vector<int> butterfly{0}; vector<vector<Complex> > zeta{{{1, 0}}}; void calc(int n) { int prev_n = butterfly.size(); if (n <= prev_n) return; butterfly.resize(n); int prev_lg = zeta.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)); zeta.resize(lg); FOR(i, prev_lg, lg) { zeta[i].resize(1 << i); Real angle = -M_PI * 2 / (1 << (i + 1)); REP(j, 1 << (i - 1)) { zeta[i][j << 1] = zeta[i - 1][j]; Real theta = angle * ((j << 1) + 1); zeta[i][(j << 1) + 1] = {cos(theta), sin(theta)}; } } } void sub_dft(vector<Complex> &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) { Complex tmp = a[i + j + block] * zeta[den][j]; a[i + j + block] = a[i + j] - tmp; a[i + j] = a[i + j] + tmp; } } } template <typename T> vector<Complex> dft(const vector<T> &a) { int sz = a.size(), lg = 1; while ((1 << lg) < sz) ++lg; vector<Complex> c(1 << lg); REP(i, sz) c[i].re = a[i]; sub_dft(c); return c; } vector<Real> real_idft(vector<Complex> &a) { int n = a.size(), half = n >> 1, quarter = half >> 1; // assert(__builtin_popcount(n) == 1); calc(n); a[0] = (a[0] + a[half] + (a[0] - a[half]).mul_pin(1)).mul_real(0.5); int den = __builtin_ctz(half); FOR(i, 1, quarter) { int j = half - i; Complex tmp1 = a[i] + a[j].conj(), tmp2 = ((a[i] - a[j].conj()) * zeta[den][j]).mul_pin(1); a[i] = (tmp1 - tmp2).mul_real(0.5); a[j] = (tmp1 + tmp2).mul_real(0.5).conj(); } if (quarter > 0) a[quarter] = a[quarter].conj(); a.resize(half); sub_dft(a); reverse(a.begin() + 1, a.end()); Real r = 1.0 / half; vector<Real> res(n); REP(i, n) res[i] = (i & 1 ? a[i >> 1].im : a[i >> 1].re) * r; return res; } void idft(vector<Complex> &a) { int n = a.size(); sub_dft(a); reverse(a.begin() + 1, a.end()); Real r = 1.0 / n; REP(i, n) a[i] = a[i].mul_real(r); } template <typename T> vector<Real> 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<Complex> c(n); REP(i, a_sz) c[i].re = a[i]; REP(i, b_sz) c[i].im = b[i]; sub_dft(c); int half = n >> 1; c[0] = Complex(c[0].re * c[0].im, 0); FOR(i, 1, half) { Complex i_square = c[i] * c[i], j_square = c[n - i] * c[n - i]; c[i] = (j_square.conj() - i_square).mul_pin(0.25); c[n - i] = (i_square.conj() - j_square).mul_pin(0.25); } c[half] = Complex(c[half].re * c[half].im, 0); vector<Real> res = real_idft(c); res.resize(sz); return res; } }; vector<ModInt> mod_convolution(const vector<ModInt> &a, const vector<ModInt> &b, const int pre = 15) { using Complex = FFT::Complex; 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<Complex> A(n), B(n); REP(i, a_sz) { int ai = a[i].val; A[i] = Complex(ai & ((1 << pre) - 1), ai >> pre); } REP(i, b_sz) { int bi = b[i].val; B[i] = Complex(bi & ((1 << pre) - 1), bi >> pre); } FFT::sub_dft(A); FFT::sub_dft(B); int half = n >> 1; Complex tmp_a = A[0], tmp_b = B[0]; A[0] = {tmp_a.re * tmp_b.re, tmp_a.im * tmp_b.im}; B[0] = {tmp_a.re * tmp_b.im + tmp_a.im * tmp_b.re, 0}; FOR(i, 1, half) { int j = n - i; Complex a_l_i = (A[i] + A[j].conj()).mul_real(0.5), a_h_i = (A[j].conj() - A[i]).mul_pin(0.5); Complex b_l_i = (B[i] + B[j].conj()).mul_real(0.5), b_h_i = (B[j].conj() - B[i]).mul_pin(0.5); Complex a_l_j = (A[j] + A[i].conj()).mul_real(0.5), a_h_j = (A[i].conj() - A[j]).mul_pin(0.5); Complex b_l_j = (B[j] + B[i].conj()).mul_real(0.5), b_h_j = (B[i].conj() - B[j]).mul_pin(0.5); A[i] = a_l_i * b_l_i + (a_h_i * b_h_i).mul_pin(1); B[i] = a_l_i * b_h_i + a_h_i * b_l_i; A[j] = a_l_j * b_l_j + (a_h_j * b_h_j).mul_pin(1); B[j] = a_l_j * b_h_j + a_h_j * b_l_j; } tmp_a = A[half]; tmp_b = B[half]; A[half] = {tmp_a.re * tmp_b.re, tmp_a.im * tmp_b.im}; B[half] = {tmp_a.re * tmp_b.im + tmp_a.im * tmp_b.re, 0}; FFT::idft(A); FFT::idft(B); vector<ModInt> res(sz); ModInt tmp1 = 1 << pre, tmp2 = 1LL << (pre << 1); REP(i, sz) { res[i] += static_cast<ll>(A[i].re + 0.5); res[i] += tmp1 * static_cast<ll>(B[i].re + 0.5); res[i] += tmp2 * static_cast<ll>(A[i].im + 0.5); } return res; } int main() { int n, m; cin >> n >> m; vector<ModInt> a(n), b(m); REP(i, n) cin >> a[i]; REP(i, m) cin >> b[i]; vector<ModInt> ans = mod_convolution(a, b); REP(i, n + m - 1) cout << ans[i] << " \n"[i + 1 == n + m - 1]; return 0; }