結果
| 問題 | No.3451 Same Numbers |
| コンテスト | |
| ユーザー |
 hos.lyric
|
| 提出日時 | 2026-02-23 06:41:28 |
| 言語 | C++14 (gcc 15.2.0 + boost 1.89.0) |
| 結果 |
WA
|
| 実行時間 | - |
| コード長 | 14,058 bytes |
| 記録 | |
| コンパイル時間 | 1,588 ms |
| コンパイル使用メモリ | 152,768 KB |
| 実行使用メモリ | 9,908 KB |
| 最終ジャッジ日時 | 2026-02-23 11:40:15 |
| 合計ジャッジ時間 | 8,431 ms |
|
ジャッジサーバーID （参考情報） |
judge4 / judge3 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| sample | AC * 3 |
| other | AC * 18 WA * 19 |
ソースコード
#include <cassert>
#include <cmath>
#include <cstdint>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <algorithm>
#include <bitset>
#include <chrono>
#include <complex>
#include <deque>
#include <functional>
#include <iostream>
#include <limits>
#include <map>
#include <numeric>
#include <queue>
#include <random>
#include <set>
#include <sstream>
#include <string>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>
using namespace std;
using Int = long long;
template <class T> ostream &operator<<(ostream &os, const vector<T> &as);
template <class T1, class T2> ostream &operator<<(ostream &os, const pair<T1, T2> &a) { return os << "(" << a.first << ", " << a.second << ")"; };
template <class T> ostream &operator<<(ostream &os, const vector<T> &as) { const int sz = as.size(); os << "["; for (int i = 0; i < sz; ++i) { if (i >= 256) { os << ", ..."; break; } if (i > 0) { os << ", "; } os << as[i]; } return os << "]"; }
template <class T> void pv(T a, T b) { for (T i = a; i != b; ++i) cerr << *i << " "; cerr << endl; }
template <class T> bool chmin(T &t, const T &f) { if (t > f) { t = f; return true; } return false; }
template <class T> bool chmax(T &t, const T &f) { if (t < f) { t = f; return true; } return false; }
#define COLOR(s) ("\x1b[" s "m")
////////////////////////////////////////////////////////////////////////////////
template <unsigned M_> struct ModInt {
static constexpr unsigned M = M_;
unsigned x;
constexpr ModInt() : x(0U) {}
constexpr ModInt(unsigned x_) : x(x_ % M) {}
constexpr ModInt(unsigned long long x_) : x(x_ % M) {}
constexpr ModInt(int x_) : x(((x_ %= static_cast<int>(M)) < 0) ? (x_ + static_cast<int>(M)) : x_) {}
constexpr ModInt(long long x_) : x(((x_ %= static_cast<long long>(M)) < 0) ? (x_ + static_cast<long long>(M)) : x_) {}
ModInt &operator+=(const ModInt &a) { x = ((x += a.x) >= M) ? (x - M) : x; return *this; }
ModInt &operator-=(const ModInt &a) { x = ((x -= a.x) >= M) ? (x + M) : x; return *this; }
ModInt &operator*=(const ModInt &a) { x = (static_cast<unsigned long long>(x) * a.x) % M; return *this; }
ModInt &operator/=(const ModInt &a) { return (*this *= a.inv()); }
ModInt pow(long long e) const {
if (e < 0) return inv().pow(-e);
ModInt a = *this, b = 1U; for (; e; e >>= 1) { if (e & 1) b *= a; a *= a; } return b;
}
ModInt inv() const {
unsigned a = M, b = x; int y = 0, z = 1;
for (; b; ) { const unsigned q = a / b; const unsigned c = a - q * b; a = b; b = c; const int w = y - static_cast<int>(q) * z; y = z; z = w; }
assert(a == 1U); return ModInt(y);
}
ModInt operator+() const { return *this; }
ModInt operator-() const { ModInt a; a.x = x ? (M - x) : 0U; return a; }
ModInt operator+(const ModInt &a) const { return (ModInt(*this) += a); }
ModInt operator-(const ModInt &a) const { return (ModInt(*this) -= a); }
ModInt operator*(const ModInt &a) const { return (ModInt(*this) *= a); }
ModInt operator/(const ModInt &a) const { return (ModInt(*this) /= a); }
template <class T> friend ModInt operator+(T a, const ModInt &b) { return (ModInt(a) += b); }
template <class T> friend ModInt operator-(T a, const ModInt &b) { return (ModInt(a) -= b); }
template <class T> friend ModInt operator*(T a, const ModInt &b) { return (ModInt(a) *= b); }
template <class T> friend ModInt operator/(T a, const ModInt &b) { return (ModInt(a) /= b); }
explicit operator bool() const { return x; }
bool operator==(const ModInt &a) const { return (x == a.x); }
bool operator!=(const ModInt &a) const { return (x != a.x); }
friend std::ostream &operator<<(std::ostream &os, const ModInt &a) { return os << a.x; }
};
////////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////////
constexpr unsigned MO = 998244353U;
constexpr unsigned MO2 = 2U * MO;
constexpr int FFT_MAX = 23;
using Mint = ModInt<MO>;
constexpr Mint FFT_ROOTS[FFT_MAX + 1] = {1U, 998244352U, 911660635U, 372528824U, 929031873U, 452798380U, 922799308U, 781712469U, 476477967U, 166035806U, 258648936U, 584193783U, 63912897U, 350007156U, 666702199U, 968855178U, 629671588U, 24514907U, 996173970U, 363395222U, 565042129U, 733596141U, 267099868U, 15311432U};
constexpr Mint INV_FFT_ROOTS[FFT_MAX + 1] = {1U, 998244352U, 86583718U, 509520358U, 337190230U, 87557064U, 609441965U, 135236158U, 304459705U, 685443576U, 381598368U, 335559352U, 129292727U, 358024708U, 814576206U, 708402881U, 283043518U, 3707709U, 121392023U, 704923114U, 950391366U, 428961804U, 382752275U, 469870224U};
constexpr Mint FFT_RATIOS[FFT_MAX] = {911660635U, 509520358U, 369330050U, 332049552U, 983190778U, 123842337U, 238493703U, 975955924U, 603855026U, 856644456U, 131300601U, 842657263U, 730768835U, 942482514U, 806263778U, 151565301U, 510815449U, 503497456U, 743006876U, 741047443U, 56250497U, 867605899U};
constexpr Mint INV_FFT_RATIOS[FFT_MAX] = {86583718U, 372528824U, 373294451U, 645684063U, 112220581U, 692852209U, 155456985U, 797128860U, 90816748U, 860285882U, 927414960U, 354738543U, 109331171U, 293255632U, 535113200U, 308540755U, 121186627U, 608385704U, 438932459U, 359477183U, 824071951U, 103369235U};
// as[rev(i)] <- \sum_j \zeta^(ij) as[j]
void fft(Mint *as, int n) {
assert(!(n & (n - 1))); assert(1 <= n); assert(n <= 1 << FFT_MAX);
int m = n;
if (m >>= 1) {
for (int i = 0; i < m; ++i) {
const unsigned x = as[i + m].x; // < MO
as[i + m].x = as[i].x + MO - x; // < 2 MO
as[i].x += x; // < 2 MO
}
}
if (m >>= 1) {
Mint prod = 1U;
for (int h = 0, i0 = 0; i0 < n; i0 += (m << 1)) {
for (int i = i0; i < i0 + m; ++i) {
const unsigned x = (prod * as[i + m]).x; // < MO
as[i + m].x = as[i].x + MO - x; // < 3 MO
as[i].x += x; // < 3 MO
}
prod *= FFT_RATIOS[__builtin_ctz(++h)];
}
}
for (; m; ) {
if (m >>= 1) {
Mint prod = 1U;
for (int h = 0, i0 = 0; i0 < n; i0 += (m << 1)) {
for (int i = i0; i < i0 + m; ++i) {
const unsigned x = (prod * as[i + m]).x; // < MO
as[i + m].x = as[i].x + MO - x; // < 4 MO
as[i].x += x; // < 4 MO
}
prod *= FFT_RATIOS[__builtin_ctz(++h)];
}
}
if (m >>= 1) {
Mint prod = 1U;
for (int h = 0, i0 = 0; i0 < n; i0 += (m << 1)) {
for (int i = i0; i < i0 + m; ++i) {
const unsigned x = (prod * as[i + m]).x; // < MO
as[i].x = (as[i].x >= MO2) ? (as[i].x - MO2) : as[i].x; // < 2 MO
as[i + m].x = as[i].x + MO - x; // < 3 MO
as[i].x += x; // < 3 MO
}
prod *= FFT_RATIOS[__builtin_ctz(++h)];
}
}
}
for (int i = 0; i < n; ++i) {
as[i].x = (as[i].x >= MO2) ? (as[i].x - MO2) : as[i].x; // < 2 MO
as[i].x = (as[i].x >= MO) ? (as[i].x - MO) : as[i].x; // < MO
}
}
// as[i] <- (1/n) \sum_j \zeta^(-ij) as[rev(j)]
void invFft(Mint *as, int n) {
assert(!(n & (n - 1))); assert(1 <= n); assert(n <= 1 << FFT_MAX);
int m = 1;
if (m < n >> 1) {
Mint prod = 1U;
for (int h = 0, i0 = 0; i0 < n; i0 += (m << 1)) {
for (int i = i0; i < i0 + m; ++i) {
const unsigned long long y = as[i].x + MO - as[i + m].x; // < 2 MO
as[i].x += as[i + m].x; // < 2 MO
as[i + m].x = (prod.x * y) % MO; // < MO
}
prod *= INV_FFT_RATIOS[__builtin_ctz(++h)];
}
m <<= 1;
}
for (; m < n >> 1; m <<= 1) {
Mint prod = 1U;
for (int h = 0, i0 = 0; i0 < n; i0 += (m << 1)) {
for (int i = i0; i < i0 + (m >> 1); ++i) {
const unsigned long long y = as[i].x + MO2 - as[i + m].x; // < 4 MO
as[i].x += as[i + m].x; // < 4 MO
as[i].x = (as[i].x >= MO2) ? (as[i].x - MO2) : as[i].x; // < 2 MO
as[i + m].x = (prod.x * y) % MO; // < MO
}
for (int i = i0 + (m >> 1); i < i0 + m; ++i) {
const unsigned long long y = as[i].x + MO - as[i + m].x; // < 2 MO
as[i].x += as[i + m].x; // < 2 MO
as[i + m].x = (prod.x * y) % MO; // < MO
}
prod *= INV_FFT_RATIOS[__builtin_ctz(++h)];
}
}
if (m < n) {
for (int i = 0; i < m; ++i) {
const unsigned y = as[i].x + MO2 - as[i + m].x; // < 4 MO
as[i].x += as[i + m].x; // < 4 MO
as[i + m].x = y; // < 4 MO
}
}
const Mint invN = Mint(n).inv();
for (int i = 0; i < n; ++i) {
as[i] *= invN;
}
}
void fft(vector<Mint> &as) {
fft(as.data(), as.size());
}
void invFft(vector<Mint> &as) {
invFft(as.data(), as.size());
}
vector<Mint> convolve(vector<Mint> as, vector<Mint> bs) {
if (as.empty() || bs.empty()) return {};
const int len = as.size() + bs.size() - 1;
int n = 1;
for (; n < len; n <<= 1) {}
as.resize(n); fft(as);
bs.resize(n); fft(bs);
for (int i = 0; i < n; ++i) as[i] *= bs[i];
invFft(as);
as.resize(len);
return as;
}
vector<Mint> square(vector<Mint> as) {
if (as.empty()) return {};
const int len = as.size() + as.size() - 1;
int n = 1;
for (; n < len; n <<= 1) {}
as.resize(n); fft(as);
for (int i = 0; i < n; ++i) as[i] *= as[i];
invFft(as);
as.resize(len);
return as;
}
// m := |as|, n := |bs|
// cs[k] = \sum[i-j=k] as[i] bs[j] (0 <= k <= m-n)
// transpose of ((multiply by bs): K^[0,m-n] -> K^[0,m-1])
vector<Mint> middle(vector<Mint> as, vector<Mint> bs) {
const int m = as.size(), n = bs.size();
assert(m >= n); assert(n >= 1);
int len = 1;
for (; len < m; len <<= 1) {}
as.resize(len, 0);
fft(as);
std::reverse(bs.begin(), bs.end());
bs.resize(len, 0);
fft(bs);
for (int i = 0; i < len; ++i) as[i] *= bs[i];
invFft(as);
as.resize(m);
as.erase(as.begin(), as.begin() + (n - 1));
return as;
}
////////////////////////////////////////////////////////////////////////////////
constexpr int LIM_INV = 400'010;
Mint inv[LIM_INV], fac[LIM_INV], invFac[LIM_INV];
void prepare() {
inv[1] = 1;
for (int i = 2; i < LIM_INV; ++i) {
inv[i] = -((Mint::M / i) * inv[Mint::M % i]);
}
fac[0] = invFac[0] = 1;
for (int i = 1; i < LIM_INV; ++i) {
fac[i] = fac[i - 1] * i;
invFac[i] = invFac[i - 1] * inv[i];
}
}
Mint binom(Int n, Int k) {
if (n < 0) {
if (k >= 0) {
return ((k & 1) ? -1 : +1) * binom(-n + k - 1, k);
} else if (n - k >= 0) {
return (((n - k) & 1) ? -1 : +1) * binom(-k - 1, n - k);
} else {
return 0;
}
} else {
if (0 <= k && k <= n) {
assert(n < LIM_INV);
return fac[n] * invFac[k] * invFac[n - k];
} else {
return 0;
}
}
}
////////////////////////////////////////////////////////////////////////////////
/*
problem
Pr[atari] = 1/(N+1-k)
atari: use k units
hazure: use 1 unit
[0, k): atari
score: max l s.t. l-th atari block starts at < M
ans = \sum[l] Pr[score = l] l^E
keep drawing
Pr[score >= l]
= Pr[l-th atari is earlier than (M-k(l-1))-th hazure]
n := (l-1) + (M-k(l-1)) - 1
= \sum[l-1<=i<=n] binom(n, i) p^i (1-p)^(n-i)
= 1 - \sum[0<=i<l-1] binom(n, i) p^i (1-p)^(n-i)
*/
int N, M, E;
int main() {
prepare();
for (; ~scanf("%d%d%d", &N, &M, &E); ) {
vector<Mint> W(M + 1);
for (int i = 0; i <= M; ++i) W[i] = Mint(i).pow(E);
for (int k = 1; k <= N; ++k) {
Mint ans = 0;
if (k <= M) {
const Mint p = Mint(N + 1 - k).inv();
const Mint q = 1 - p;
const int maxL = (M + k - 1) / k;
vector<Mint> pp(maxL + 1, 0);
pp[0] = 1;
for (int l = 1; l <= maxL; ++l) pp[l] = pp[l - 1] * p;
vector<Mint> probs(maxL + 2, 0);
// O(M) vs O((M/k)^2)
if ((Int)k*k < M) {
vector<Mint> qq(M + 1);
qq[0] = 1;
for (int i = 1; i <= M; ++i) qq[i] = qq[i - 1] * q;
// \sum[0<=i<m] binom(n, i) p^i q^(n-i), q^(n-m)
int n = (maxL-1) + (M-k*(maxL-1)) - 1, m = maxL - 1;
Mint now = 0;
for (int i = 0; i < m; ++i) now += binom(n, i) * pp[i] * qq[n - i];
for (int l = maxL; l >= 1; --l) {
for (; n < (l-1) + (M-k*(l-1)) - 1; ++n) {
const int i = m - 1;
now -= (binom(n, i) * pp[i] * qq[n - i]) * p;
}
for (; m > l-1; --m) {
const int i = m - 1;
now -= binom(n, i) * pp[i] * qq[n - i];
}
probs[l] = 1 - now;
}
} else {
for (int l = 1; l <= maxL; ++l) {
probs[l] = 1;
const int n = (l-1) + (M-k*(l-1)) - 1;
Mint qq = q.pow(n - (l-1));
for (int i = l-1; --i >= 0; ) {
qq *= q;
probs[l] -= binom(n, i) * pp[i] * qq;
}
}
}
// cerr<<"k = "<<k<<": probs = "<<probs<<endl;
for (int l = 1; l <= maxL; ++l) ans += (probs[l] - probs[l + 1]) * W[l];
}
printf("%u\n", ans.x);
}
}
return 0;
}
/*
3 3 2
1 2 100000
9 24 167
k = 1: probs = [0, 1, 221832079, 443664157, 0]
887328317
k = 2: probs = [0, 1, 499122177, 0]
499122179
k = 3: probs = [0, 1, 0]
1
k = 1: probs = [0, 1, 1, 0]
538261388
k = 1: probs = [0, 1, 693308781, 190960641, 997598478, 330820600, 662767691, 995135321, 870212094, 315341003, 925306495, 220512345, 346734457, 456130392, 594585428, 33319507, 642760783, 788293314, 610218281, 300111342, 79222646, 19417394, 117746698, 689927923, 322088350, 0]
266696013
k = 2: probs = [0, 1, 25813421, 403216879, 640785363, 944675728, 519485056, 698821010, 288018657, 181596768, 33347964, 232561991, 234329087, 0]
354954351
k = 3: probs = [0, 1, 608032416, 532164453, 290859902, 991216413, 728203815, 739321606, 504556086, 0]
889968913
k = 4: probs = [0, 1, 90863669, 352250157, 121596464, 625663189, 690868731, 0]
422652273
k = 5: probs = [0, 1, 89769263, 844106082, 322101439, 25107842, 0]
484325722
k = 6: probs = [0, 1, 725187494, 126482959, 677351809, 0]
488941374
k = 7: probs = [0, 1, 389223540, 375580655, 61620022, 0]
396408879
k = 8: probs = [0, 1, 15233, 19496961, 0]
596917142
k = 9: probs = [0, 1, 1, 1, 0]
76920761
*/