結果

問題 No.3095 Many Min Problems
ユーザー Kude
提出日時 2025-04-06 16:39:20
言語 C++23
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 113 ms / 2,000 ms
コード長 3,379 bytes
コンパイル時間 4,192 ms
コンパイル使用メモリ 309,072 KB
実行使用メモリ 19,836 KB
最終ジャッジ日時 2025-04-06 16:39:28
合計ジャッジ時間 7,065 ms
ジャッジサーバーID
（参考情報） 		judge1 / judge4
このコードへのチャレンジ
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ファイルパターン 結果
sample AC * 3
other AC * 30
権限があれば一括ダウンロードができます
コンパイルメッセージ
main.cpp:49:6: warning: ‘{anonymous}::mint {anonymous}::perm(int, int)’ defined but not used [-Wunused-function]
   49 | mint perm(int n, int k) {
      |      ^~~~
main.cpp:48:6: warning: ‘{anonymous}::mint {anonymous}::fact(int)’ defined but not used [-Wunused-function]
   48 | mint fact(int n) {return Fact[n];}
      |      ^~~~
main.cpp:44:6: warning: ‘{anonymous}::mint {anonymous}::icomb(int, int)’ defined but not used [-Wunused-function]
   44 | mint icomb(int n, int k) {
      |      ^~~~~
main.cpp:37:6: warning: ‘{anonymous}::mint {anonymous}::comb(int, int)’ defined but not used [-Wunused-function]
   37 | mint comb(int n, int k) {
      |      ^~~~

ソースコード

diff # 

#include<bits/stdc++.h>
namespace {
#pragma GCC diagnostic ignored "-Wunused-function"
#include<atcoder/all>
#pragma GCC diagnostic warning "-Wunused-function"
using namespace std;
using namespace atcoder;
#define rep(i,n) for(int i = 0; i < (int)(n); i++)
#define rrep(i,n) for(int i = (int)(n) - 1; i >= 0; i--)
#define all(x) begin(x), end(x)
#define rall(x) rbegin(x), rend(x)
template<class T> bool chmax(T& a, const T& b) { if (a < b) { a = b; return true; } else return false; }
template<class T> bool chmin(T& a, const T& b) { if (b < a) { a = b; return true; } else return false; }
using ll = long long;
using P = pair<int,int>;
using VI = vector<int>;
using VVI = vector<VI>;
using VL = vector<ll>;
using VVL = vector<VL>;
using mint = modint998244353;

constexpr int FACT_SIZE = 1000000;
mint Fact[FACT_SIZE + 1];
mint iFact[FACT_SIZE + 1];
const auto fact_init = [] {
    Fact[0] = mint::raw(1);
    for(int i = 1; i <= FACT_SIZE; ++i) {
        Fact[i] = Fact[i-1] * i;
    }
    iFact[FACT_SIZE] = Fact[FACT_SIZE].inv();
    for(int i = FACT_SIZE; i; --i) {
        iFact[i-1] = iFact[i] * i;
    }
    return false;
}();

mint comb(int n, int k) {
    if (k == 0) return mint::raw(1);
    assert(n >= 0 && k >= 0);
    if (k > n) return mint::raw(0);
    return Fact[n] * iFact[n - k] * iFact[k];
}

mint icomb(int n, int k) {
    return iFact[n] * Fact[n - k] * Fact[k];
}

mint fact(int n) {return Fact[n];}
mint perm(int n, int k) {
    assert(0 <= n);
    return Fact[n] * iFact[n - k];
}


vector<mint> fps_inv(vector<mint> f, int precision=-1) {
  if (precision == -1) precision = f.size();
  assert(precision >= 1 && f.size() >= 1 && f[0] != 0);
  auto f0 = f[0];
  if (f0 != 1) {
    f0 = f0.inv();
    for (auto& x : f) x *= f0;
  }
  int sz_tgt = bit_ceil(0U + precision);
  vector<mint> g(sz_tgt), g_ftt, fg;
  g_ftt.reserve(sz_tgt), fg.reserve(sz_tgt);
  g[0] = 1;
  static_assert(mint::mod() > 1 && (mint::mod() - 1) % 4 == 0);
  const mint i4 = mint::raw(mint::mod() - (mint::mod() - 1) / 4);
  mint iz = -1;
  for (int n = 1; n < sz_tgt; n *= 2) {
    fg.assign(f.begin(), f.begin() + min<int>(2 * n, f.size())), fg.resize(2 * n);
    g_ftt.assign(g.begin(), g.begin() + 2 * n);
    internal::butterfly(fg), internal::butterfly(g_ftt);
    for (int i = 0; i < 2 * n; i++) fg[i] *= g_ftt[i];
    internal::butterfly_inv(fg);
    for (int i = 0; i < n; i++) fg[i] = 0;
    internal::butterfly(fg);
    for (int i = 0; i < 2 * n; i++) fg[i] *= g_ftt[i];
    internal::butterfly_inv(fg);
    iz *= i4;
    for (int i = n; i < 2 * n; i++) g[i] = fg[i] * iz;
  }
  g.resize(precision);
  if (f0 != 1) for (auto& x : g) x *= f0;
  return g;
}


// 0^k+1^k+...+(n-1)^k for each k in [0,m)
vector<mint> kth_power_sums(mint n, int m) {
  // e^0+e^x+e^2x+...+e^(n-1)x
  // = ((e^nx-1)/x) / ((e^x-1)/x)
  // =: f / g
  if (m == 0) return {};
  vector<mint> f(m), g(m);
  mint pow_n = n;
  for (int i = 0; i < m; i++) {
    f[i] = pow_n * iFact[i + 1];
    g[i] = iFact[i + 1];
    pow_n *= n;
  }
  vector<mint> res = convolution(f, fps_inv(g));
  res.resize(m);
  for (int i = 0; i < m; i++) res[i] *= Fact[i];
  return res;
}

} int main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  int n, m;
  cin >> n >> m;
  auto s = kth_power_sums(m + 1, n + 1);
  mint ans;
  rep(i, n + 1) if (i) {
    ans *= m;
    ans += s[i];
  }
  cout << ans.val() << '\n';
}
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