# Submit Info #40155

Problem Lang User Status Time Memory
Partition Function cpp DivineJK AC 1462 ms 45.57 MiB

ケース詳細
Name Status Time Memory
0_00 AC 2 ms 0.67 MiB
100000_00 AC 238 ms 12.46 MiB
10000_00 AC 21 ms 1.95 MiB
1000_00 AC 2 ms 0.79 MiB
100_00 AC 1 ms 0.65 MiB
1_00 AC 1 ms 0.64 MiB
200000_00 AC 585 ms 23.13 MiB
300000_00 AC 1403 ms 43.35 MiB
400000_00 AC 1458 ms 44.42 MiB
500000_00 AC 1462 ms 45.57 MiB
example_00 AC 2 ms 0.67 MiB

#include <bits/stdc++.h> using namespace std; const int mod_hand = 998244353; const int root_hand = 128805723; const int invr_hand = 31; long long safety_divide(long long a, long long b, bool mod=false){ long long r, m; r = a / b; m = a % b; if (m < 0){ if (b > 0){ m += b; r -= 1; } else{ m -= b; r += 1; } } if (mod){ return m; } return r; } int modpow(int n, int m, int mod){ int y = 1, bas = n; while (m){ if (m & 1){ y = (long long)y * bas % mod; } bas = (long long)bas * bas % mod; m >>= 1; } return y; } bool IsPrime(int n){ if (n == 1) return false; int p = 2; while (p * p <= n){ if (n % p == 0) return false; p++; } return true; } template<typename T> void vec_out(vector<T> v, int l=0, int r=1<<30){ int n = min((int)v.size(), r); if (l >= n){ printf("\n"); return; } printf("%d", v[l]); for (int i=l+1;i<n;i++){ printf(" %d", v[i]); } printf("\n"); } int sqrt_mod(int p, int y){ if (y == 0) return 0; if (p == 2) return y & 1; int c = modpow(y, (p - 1) / 2, p); if (c == p - 1) return -1; int q = p - 1; int m = 0, b; while (q % 2 == 0){ q >>= 1; m++; } int z = 1; while (modpow(z, (p-1)/2, p) == 1){ z++; } int t = modpow(y, q, p), r = modpow(y, (q+1)/2, p); c = modpow(z, q, p); int cnt; while (t - 1){ cnt = 0, b = t; while (b - 1){ b = (long long)b * b % p; cnt++; } b = modpow(c, 1<<(m-cnt-1), p); m = cnt, c = (long long)b * b % p, t = (long long) t * c % p, r = (long long)r * b % p; } return r; } int inved(long long a, long long MOD=mod_hand){ long long x = 1, y = 0, u = 0, v = 1, k = a, l = MOD; long long tmp1, tmp2, tmp3; while (l){ tmp1 = x; tmp2 = y; x = u; y = v; u = (long long)tmp1 - u * safety_divide(k, l); v = (long long)tmp2 - v * safety_divide(k, l); tmp3 = k; k = l; l = safety_divide(tmp3, l, true); } if (x < 0){x+=MOD;} return x; } vector<int> ntt_hand(vector<int> f, int n, int root=root_hand){ int depth = 0; int bin_top = 1; while (bin_top < n){ bin_top <<= 1; depth++; } int pos = 0, tmp = 0, d = 0; vector<int> res(bin_top, 0); for (int i=0;i<n-1;i++){ res[i] = f[pos]; tmp = (i+1)&-(i+1); d = 0; while (tmp){ d++; tmp >>= 1; } pos ^= (n-(1<<(depth-d))); } int MOD = mod_hand; res[n-1] = f[pos]; vector<int> base_list(24); base_list[23] = root; for (int i=23;i>0;i--){ base_list[i-1] = (long long)base_list[i]*base_list[i]%MOD; } int grow = 1, seed = 1, offset = 1; int u, v; for (int i=0;i<depth;i++){ grow = 1; seed = base_list[i+1]; offset = 1 << i; for (int k=0;k<offset;k++){ for (int j=k;j<n;j+=1<<(i+1)){ u = res[j]; v = (long long)res[j+offset] * grow % MOD; res[j] = (u+v>=MOD ? u+v-MOD : u+v); res[j+offset] = (u-v<0 ? u-v+MOD : u-v); } grow = (long long)grow * seed % MOD; } } return res; } vector<int> inv_ntt_hand(vector<int> f, int n){ vector<int> res = ntt_hand(f, n, invr_hand); int MOD = mod_hand; int x = inved(n); for (int i=0;i<n;i++){ res[i] = (long long)res[i] * x % MOD; } return res; } vector<int> convolute_one(vector<int> f, vector<int> g){ int n = f.size(); int m = g.size(); int MOD = mod_hand; int bin_top = 1; while (bin_top < n + m){ bin_top <<= 1; } vector<int> x(bin_top); vector<int> y(bin_top); for (int i=0;i<n;i++){ x[i] = f[i]; } for (int i=0;i<m;i++){ y[i] = g[i]; } x = ntt_hand(x, bin_top); y = ntt_hand(y, bin_top); for (int i=0;i<bin_top;i++){ x[i] = (long long)x[i] * y[i] % MOD; } return inv_ntt_hand(x, bin_top); } vector<int> ntt_free(vector<int> f, int n, int MOD, int root){ int depth = 0; int bin_top = 1; while (bin_top < n){ bin_top <<= 1; depth++; } int pos = 0, tmp = 0, d = 0; vector<int> res(bin_top, 0); for (int i=0;i<n-1;i++){ res[i] = f[pos]; tmp = (i+1)&-(i+1); d = 0; while (tmp){ d++; tmp >>= 1; } pos ^= (n-(1<<(depth-d))); } res[n-1] = f[pos]; vector<int> base_list(24); base_list[23] = root; for (int i=23;i>0;i--){ base_list[i-1] = (long long)base_list[i]*base_list[i]%MOD; } int grow = 1, seed = 1, offset = 1; int u, v; for (int i=0;i<depth;i++){ grow = 1; seed = base_list[i+1]; offset = 1 << i; for (int k=0;k<offset;k++){ for (int j=k;j<n;j+=1<<(i+1)){ u = res[j]; v = (long long)res[j+offset] * grow % MOD; res[j] = (u+v>=MOD ? u+v-MOD : u+v); res[j+offset] = (u-v<0 ? u-v+MOD : u-v); } grow = (long long)grow * seed % MOD; } } return res; } vector<int> inv_ntt_free(vector<int> f, int n, int MOD, int invr_free){ vector<int> res = ntt_free(f, n, MOD, invr_free); int x = inved(n, MOD); for (int i=0;i<n;i++){ res[i] = (int)((long long)res[i] * x % MOD); } return res; } vector<int> convolute_general(vector<int> f, vector<int> g, int MOD, int convolute_rank=3, int binary_rank=23, int modulo_limit=(int)1e8){ int n = f.size(); int m = g.size(); int bin_top = 1; while (bin_top < n + m){ bin_top <<= 1; } vector<int> res(bin_top, 0); int s = 0; if ((long long)n * m <= 524288){ for (int i=0;i<n;i++){ for (int j=0;j<m;j++){ s = (long long)f[i] * g[j] % MOD; res[i+j] = (res[i+j] + s >= MOD ? res[i+j] + s - MOD : res[i+j] + s); } } return res; } vector<int> x(bin_top); vector<int> y(bin_top); for (int i=0;i<n;i++){ x[i] = f[i]; } for (int i=0;i<m;i++){ y[i] = g[i]; } vector<int> mod_list(convolute_rank, 0); vector<int> primitive_root_list(convolute_rank, 0); int mod_cnt = 0, r = 0; bool flg, fflg; int b = (1 << binary_rank); int odd_part = (modulo_limit + b - 1) / b; if (odd_part & ~1) odd_part++; while (mod_cnt < convolute_rank){ if (IsPrime(odd_part*b+1)){ r = 1; flg = true; while (flg){ fflg = true; for (int i=0;i<binary_rank;i++){ if (modpow(r, 1<<i, odd_part*b+1) == 1) fflg = false; } if (modpow(r, 1<<binary_rank, odd_part*b+1) != 1) fflg = false; if (fflg){ mod_list[mod_cnt] = odd_part*b+1; primitive_root_list[mod_cnt] = r; flg = false; mod_cnt++; } r++; } } odd_part++; } vector<vector<int>> res_x(convolute_rank, vector<int>(bin_top, 0)); vector<vector<int>> res_y(convolute_rank, vector<int>(bin_top, 0)); for (int i=0;i<convolute_rank;i++){ res_x[i] = ntt_free(x, bin_top, mod_list[i], inved(primitive_root_list[i], mod_list[i])); res_y[i] = ntt_free(y, bin_top, mod_list[i], inved(primitive_root_list[i], mod_list[i])); for (int j=0;j<bin_top;j++){ res_x[i][j] = (long long)res_x[i][j] * res_y[i][j] % mod_list[i]; } res_x[i] = inv_ntt_free(res_x[i], bin_top, mod_list[i], primitive_root_list[i]); } for (int i=1;i<convolute_rank;i++){ for (int j=0;j<bin_top;j++){ for (int k=0;k<i;k++){ res_x[i][j] = (res_x[i][j] - res_x[k][j] >= 0 ? res_x[i][j] - res_x[k][j] : res_x[i][j] - res_x[k][j] + mod_list[i]); res_x[i][j] = (long long)res_x[i][j] * inved(mod_list[k], mod_list[i]) % mod_list[i]; } } } int tmp = 1; for (int i=0;i<convolute_rank;i++){ for (int j=0;j<bin_top;j++){ s = (long long)tmp * res_x[i][j] % MOD; res[j] = (res[j] + s >= MOD ? res[j] + s - MOD : res[j] + s); } tmp = (long long) tmp * mod_list[i] % MOD; } return res; } vector<int> inverse(vector<int> f, int MOD=mod_hand){ int n = f.size(); vector<int> g(1, inved(f[0])); int bin_top = 1; while (bin_top < n){ bin_top <<= 1; } vector<int> t(bin_top); for (int i=0;i<n;i++){ t[i] = f[i]; } vector<int> x(1, f[0]); vector<int> tmp; vector<int> h; int m = 1; while (m < n){ for (int i=0;i<m;i++){x.push_back(t[i+m]);} m <<= 1; h = convolute_one(x, g); h.resize(m); h[0] = (2 - h[0]); if (h[0] < 0){h[0] += MOD;} for (int i=1;i<m;i++){ h[i] = (h[i] ? MOD - h[i] : 0); } g = convolute_one(g, h); g.resize(m); } return g; } vector<int> differentiate(vector<int> f, int MOD=mod_hand){ int n = f.size(); vector<int> res(n); for (int i=1;i<n;i++){ res[i-1] = (long long)f[i] * i % MOD; } return res; } vector<int> integrate(vector<int> f, int MOD=mod_hand){ int n = f.size(); vector<int> res(n); vector<int> invn(n+1, 1); for (int i=0;i<n-1;i++){ res[i+1] = (long long)f[i] * invn[i+1] % MOD; invn[i+2] = (long long)(MOD - invn[MOD%(i+2)]) * (MOD/(i+2)) % MOD; } return res; } vector<int> logarithm(vector<int> f, int MOD=mod_hand){ int n = f.size(); vector<int> res = differentiate(f); res = convolute_one(res, inverse(f)); res.resize(n); res = integrate(res); return res; } vector<int> exponential(vector<int> f, int MOD=mod_hand){ int n = f.size(); int bin_top = 1; while (bin_top < n){ bin_top <<= 1; } vector<int> t(bin_top); for (int i=0;i<n;i++){ t[i] = f[i]; } vector<int> g(1, 1); vector<int> p(1, 1); int m = 1; vector<int> h, w, q, r, x; while (2*m <= bin_top){ h = convolute_one(g, p); h.resize(m); h[0] = (2 - h[0] < 0 ? 2 - h[0] + MOD : 2 - h[0]); for (int i=1;i<m;i++){ h[i] = (h[i] ? MOD - h[i] : 0); } g = convolute_one(g, h); g.resize(m); q.resize(m); for (int i=0;i<m;i++){ q[i] = t[i]; } q = differentiate(q); r = convolute_one(p, q); r.resize(2*m); for (int i=1;i<m;i++){ r[i-1] = (long long)i * p[i] % MOD - r[i-1]; r[i-1] = (r[i-1] < 0 ? r[i-1] + MOD : r[i-1]); } for (int i=m;i<2*m;i++){ r[i-1] = (r[i-1] ? MOD - r[i-1] : 0); } w = convolute_one(g, r); w.resize(2*m); for (int i=0;i<m;i++){ w[i] = (w[i] + q[i] >= MOD ? w[i] + q[i] - MOD : w[i] + q[i]); } w = integrate(w); for (int i=0;i<2*m;i++){ w[i] = (t[i] > w[i] ? t[i] - w[i] : t[i] - w[i] + MOD); } x = convolute_one(p, w); for (int i=0;i<m;i++){ p[i] = (p[i] + x[i] >= MOD ? p[i] + x[i] - MOD : p[i] + x[i]); p.push_back(x[i+m]); } m <<= 1; } return p; } vector<int> pow_of_fps(vector<int> f, int m, int MOD=mod_hand){ int n = f.size(); int nonzero_pos = 0; while (f[nonzero_pos] == 0){ nonzero_pos++; if (nonzero_pos == n){ break; } } vector<int> res(n, 0); if ((long long)nonzero_pos*m >= n){ return res; } int v = inved(f[nonzero_pos]); int b = f[nonzero_pos]; for (int i=nonzero_pos;i<n;i++){ res[i-nonzero_pos] = (long long)v * f[i] % MOD; } res = logarithm(res); for (int i=0;i<n;i++){ res[i] = (long long)m * res[i] % MOD; } int c = 1, tmp = nonzero_pos * m; while (m){ if (m & 1){ c = (long long)c * b % MOD; } b = (long long) b * b % MOD; m >>= 1; } res = exponential(res); for (int i=0;i<n;i++){ res[i] = (long long)res[i] * c % MOD; } for (int i=n;i>tmp;i--){ res[i-1] = res[i-tmp-1]; } for (int i=0;i<tmp;i++){ res[i] = 0; } return res; } vector<int> sqrt_of_fps(vector<int> f, int MOD=mod_hand){ int n = f.size(); vector<int> g = {1}; vector<int> res(n, 0); int nonzero_pos = 0; while (f[nonzero_pos] == 0){ nonzero_pos++; if (nonzero_pos == n) break; } if (nonzero_pos == n) return res; if (nonzero_pos & 1) return {-1}; int s = sqrt_mod(MOD, f[nonzero_pos]); if (s == -1) return {-1}; g[0] = s; int bin_top = 1; while (bin_top < n){ bin_top <<= 1; } vector<int> t(bin_top, 0); for (int i=nonzero_pos;i<n;i++){ t[i-nonzero_pos] = f[i]; } int m = 1, i2 = inved(2); vector<int> u(1, t[0]), v; while (m <= bin_top){ v = convolute_one(inverse(g), u); for (int i=0;i<m;i++){ u.push_back(t[i+m]); } m <<= 1; g.resize(m); for (int i=0;i<m;i++){ g[i] = (v[i] + g[i] >= MOD ? v[i] + g[i] - MOD : v[i] + g[i]); g[i] = (long long)g[i] * i2 % MOD; } } for (int i=n-nonzero_pos/2;i>0;i--){ g[i+nonzero_pos/2-1] = g[i-1]; } for (int i=0;i<nonzero_pos/2;i++){ g[i] = 0; } return g; } vector<int> polynomial_taylor_shift(vector<int> f, int c, int MOD=mod_hand){ int n = f.size(); vector<int> invn(n+1, 1); int fact = 1; int invf = 1; vector<int> invf_list(n+1, 1); int tmp = 1; vector<int> x(n); vector<int> y(n); c = safety_divide(c, MOD, true); for (int i=0;i<n;i++){ x[n-i-1] = (long long)f[i] * fact % MOD; y[i] = (long long)tmp * invf % MOD; if (i){ invn[i+1] = (long long)(MOD - invn[MOD%(i+1)]) * (MOD/(i+1)) % MOD; } fact = (long long)fact * (i+1) % MOD; invf = (long long)invf * invn[i+1] % MOD; invf_list[i+1] = invf; tmp = (long long)tmp * c % MOD; } x = convolute_one(x, y); x.resize(n); for (int i=0;2*i<n;i++){ tmp = x[i]; x[i] = x[n-i-1]; x[n-i-1] = tmp; } for (int i=0;i<n;i++){ x[i] = (long long)x[i] * invf_list[i] % MOD; } return x; } vector<int> subset_sum(vector<int> f, int t, int MOD=mod_hand){ vector<int> num_cnt(t+1, 0); for (int i: f) num_cnt[i]++; vector<int> invn(t+1, 1); for (int i=2;i<=t;i++){ invn[i] = (long long)(MOD - invn[MOD%i]) * (MOD/i) % MOD; } vector<int> g(t+1, 0); int tmp, sign; for (int i=1;i<=t;i++){ if (num_cnt[i] == 0) continue; sign = 1; for (int j=1;i*j<=t;j++){ tmp = (long long)invn[j] * sign % MOD; tmp = (long long)tmp * num_cnt[i] % MOD; g[i*j] = (g[i*j] + tmp >= MOD ? g[i*j] + tmp - MOD : g[i*j] + tmp); sign = MOD - sign; } } return exponential(g); } vector<int> first_stirling(int n, int MOD=mod_hand){ vector<int> g = {1}; vector<int> h = {0, 1}; int m = 0; int b = 1; while (m < n){ if (b & n){ g = convolute_one(g, polynomial_taylor_shift(h, MOD - m)); m += b; g.resize(m+1); } h = convolute_one(h, polynomial_taylor_shift(h, MOD - b)); b <<= 1; h.resize(b+1); } return g; } vector<int> second_stirling(int n, int MOD=mod_hand){ vector<int> g(n+1, 0); vector<int> h(n+1, 0); vector<int> invn(n+3, 1); int tmp = 1, sign = 1; for (int i=0;i<=n;i++){ invn[i+2] = (long long)(MOD - invn[MOD%(i+2)]) * (MOD/(i+2)) % MOD; g[i] = (long long)sign * tmp % MOD; h[i] = (long long)modpow(i, n, MOD) * tmp % MOD; tmp = (long long)tmp * invn[i+1] % MOD; sign = MOD - sign; } g = convolute_one(g, h); g.resize(n+1); return g; } vector<int> partition_number(int n, int MOD=mod_hand){ vector<int> invn(n+2, 1); for (int i=2;i<n;i++){ invn[i] = (long long)(MOD - invn[MOD%i]) * (MOD/i) % MOD; } vector<int> g(n+1, 0); for (int i=1;i<=n;i++){ for (int j=1;i*j<=n;j++){ g[i*j] = (g[i*j] + invn[j] >= MOD ? g[i*j] + invn[j] - MOD : g[i*j] + invn[j]); } } g = exponential(g); return g; } int main(void){ // Your code here! int N; scanf("%d", &N); vector<int> X = partition_number(N+1); vec_out(X, 0, N+1); return 0; }