#1195523 (C++23(gcc16)) No.2846 Birthday Cake

• 問題: No.2846 Birthday Cake
• ユーザー: C
• 提出日時: 2026-10-26 23:15:51
• 言語: C++23(gcc16) (gcc 16.2.0 + boost 1.92.0 + ACL)
• 結果: AC
• 実行時間: 7 ms / 2,000 ms
• コード長: 12,621 bytes
• コンパイル時間: 7,481 ms
• コンパイル使用メモリ: 393,900 KB
• 実行使用メモリ: 9,924 KB
• 最終ジャッジ日時: 2026-10-26 23:16:02
• 合計ジャッジ時間: 9,568 ms
• ジャッジサーバーID （参考情報）: judge5_0 / judge4_0

ファイルパターン	結果
sample	AC * 3
other	AC * 31

ソースコード

#include <bits/stdc++.h>
#include <atcoder/all>
#include <boost/polygon/point_data.hpp>
#include <boost/polygon/voronoi.hpp>
#define rep(i,a,b) for(int i=(a);i<(b);i++)
#define rrep(i,a,b) for(int i=(b)-1;i>=(a);i--)
#define all(x) begin(x),end(x)
#define sz(x) (int)(x).size()
using namespace std;
using namespace atcoder;
using ll=long long;
using ld=long double;
using vll=vector<ll>;
using vvll=vector<vll>;
using vi=vector<int>;
using vvi=vector<vi>;
using pll=pair<ll,ll>;
using pi=pair<int,int>;

// using mint=modint998244353;
// using mint=modint1000000007;
// using mint2=static_modint<2>;

// using BoostPoint=boost::polygon::point_data<int>;
// using Voronoi=boost::polygon::voronoi_diagram<double>;

#line 2 "modint/modint-2-61m1.hpp"

#include <cassert>
#include <ostream>
using namespace std;

struct modint_2_61m1 {
  using M = modint_2_61m1;
  using u64 = unsigned long long;
  using u128 = __uint128_t;

  static constexpr u64 mod = (1uLL << 61) - 1;
  u64 x;

  static constexpr u64 modulo(u128 y) {
    u64 val = (y >> 61) + (y & mod);
    return val >= mod ? val - mod : val;
  }

  modint_2_61m1() : x(0) {}
  modint_2_61m1(long long _x) {
    long long y = _x % (long long)mod;
    if (y < 0) y += mod;
    x = y;
  }

  static M raw(u64 y) {
    M res;
    res.x = y;
    return res;
  }
  u64 get() const { return x; }
  static u64 get_mod() { return mod; }

  friend M operator+(const M& l, const M& r) {
    u64 y = l.x + r.x;
    if (y >= mod) y -= mod;
    return raw(y);
  }
  friend M operator-(const M& l, const M& r) {
    u64 y = l.x - r.x;
    if (y >= mod) y += mod;
    return raw(y);
  }
  friend M operator*(const M& l, const M& r) {
    return raw(modulo(u128(l.x) * r.x));
  }
  friend M operator/(const M& l, const M& r) { return l * r.inverse(); }

  M& operator+=(const M& r) { return *this = *this + r; }
  M& operator-=(const M& r) { return *this = *this - r; }
  M& operator*=(const M& r) { return *this = *this * r; }
  M& operator/=(const M& r) { return *this = *this / r; }
  M operator-() const { return raw(x ? mod - x : u64{0}); }
  M operator+() const { return *this; }

  M pow(u64 e) const {
    M res{1}, a{*this};
    while (e) {
      if (e & 1) res = res * a;
      a = a * a;
      e >>= 1;
    }
    return res;
  }
  M inverse() const {
    assert(x != 0);
    return this->pow(mod - 2);
  }

  friend bool operator==(const M& l, const M& r) { return l.x == r.x; }
  friend bool operator!=(const M& l, const M& r) { return l.x != r.x; }
  friend ostream& operator<<(ostream& os, const M& r) { return os << r.x; }
};

#line 2 "fps/sparse-fps.hpp"

#include <utility>
#include <vector>
using namespace std;

#line 2 "fps/formal-power-series.hpp"

template <typename mint>
struct FormalPowerSeries : vector<mint> {
  using vector<mint>::vector;
  using FPS = FormalPowerSeries;

  FPS &operator+=(const FPS &r) {
    if (r.size() > this->size()) this->resize(r.size());
    for (int i = 0; i < (int)r.size(); i++) (*this)[i] += r[i];
    return *this;
  }

  FPS &operator+=(const mint &r) {
    if (this->empty()) this->resize(1);
    (*this)[0] += r;
    return *this;
  }

  FPS &operator-=(const FPS &r) {
    if (r.size() > this->size()) this->resize(r.size());
    for (int i = 0; i < (int)r.size(); i++) (*this)[i] -= r[i];
    return *this;
  }

  FPS &operator-=(const mint &r) {
    if (this->empty()) this->resize(1);
    (*this)[0] -= r;
    return *this;
  }

  FPS &operator*=(const mint &v) {
    for (int k = 0; k < (int)this->size(); k++) (*this)[k] *= v;
    return *this;
  }

  FPS &operator/=(const FPS &r) {
    if (this->size() < r.size()) {
      this->clear();
      return *this;
    }
    int n = this->size() - r.size() + 1;
    if ((int)r.size() <= 64) {
      FPS f(*this), g(r);
      g.shrink();
      mint coeff = g.back().inverse();
      for (auto &x : g) x *= coeff;
      int deg = (int)f.size() - (int)g.size() + 1;
      int gs = g.size();
      FPS quo(deg);
      for (int i = deg - 1; i >= 0; i--) {
        quo[i] = f[i + gs - 1];
        for (int j = 0; j < gs; j++) f[i + j] -= quo[i] * g[j];
      }
      *this = quo * coeff;
      this->resize(n, mint(0));
      return *this;
    }
    return *this = ((*this).rev().pre(n) * r.rev().inv(n)).pre(n).rev();
  }

  FPS &operator%=(const FPS &r) {
    *this -= *this / r * r;
    shrink();
    return *this;
  }

  FPS operator+(const FPS &r) const { return FPS(*this) += r; }
  FPS operator+(const mint &v) const { return FPS(*this) += v; }
  FPS operator-(const FPS &r) const { return FPS(*this) -= r; }
  FPS operator-(const mint &v) const { return FPS(*this) -= v; }
  FPS operator*(const FPS &r) const { return FPS(*this) *= r; }
  FPS operator*(const mint &v) const { return FPS(*this) *= v; }
  FPS operator/(const FPS &r) const { return FPS(*this) /= r; }
  FPS operator%(const FPS &r) const { return FPS(*this) %= r; }
  FPS operator-() const {
    FPS ret(this->size());
    for (int i = 0; i < (int)this->size(); i++) ret[i] = -(*this)[i];
    return ret;
  }

  void shrink() {
    while (this->size() && this->back() == mint(0)) this->pop_back();
  }

  FPS rev() const {
    FPS ret(*this);
    reverse(begin(ret), end(ret));
    return ret;
  }

  FPS dot(FPS r) const {
    FPS ret(min(this->size(), r.size()));
    for (int i = 0; i < (int)ret.size(); i++) ret[i] = (*this)[i] * r[i];
    return ret;
  }

  // 前 sz 項を取ってくる。sz に足りない項は 0 埋めする
  FPS pre(int sz) const {
    FPS ret(begin(*this), begin(*this) + min((int)this->size(), sz));
    if ((int)ret.size() < sz) ret.resize(sz);
    return ret;
  }

  FPS operator>>(int sz) const {
    if ((int)this->size() <= sz) return {};
    FPS ret(*this);
    ret.erase(ret.begin(), ret.begin() + sz);
    return ret;
  }

  FPS operator<<(int sz) const {
    FPS ret(*this);
    ret.insert(ret.begin(), sz, mint(0));
    return ret;
  }

  FPS diff() const {
    const int n = (int)this->size();
    FPS ret(max(0, n - 1));
    mint one(1), coeff(1);
    for (int i = 1; i < n; i++) {
      ret[i - 1] = (*this)[i] * coeff;
      coeff += one;
    }
    return ret;
  }

  FPS integral() const {
    const int n = (int)this->size();
    FPS ret(n + 1);
    ret[0] = mint(0);
    if (n > 0) ret[1] = mint(1);
    auto mod = mint::get_mod();
    for (int i = 2; i <= n; i++) ret[i] = (-ret[mod % i]) * (mod / i);
    for (int i = 0; i < n; i++) ret[i + 1] *= (*this)[i];
    return ret;
  }

  mint eval(mint x) const {
    mint r = 0, w = 1;
    for (auto &v : *this) r += w * v, w *= x;
    return r;
  }

  FPS log(int deg = -1) const {
    assert(!(*this).empty() && (*this)[0] == mint(1));
    if (deg == -1) deg = (int)this->size();
    return (this->diff() * this->inv(deg)).pre(deg - 1).integral();
  }

  FPS pow(int64_t k, int deg = -1) const {
    const int n = (int)this->size();
    if (deg == -1) deg = n;
    if (k == 0) {
      FPS ret(deg);
      if (deg) ret[0] = 1;
      return ret;
    }
    for (int i = 0; i < n; i++) {
      if ((*this)[i] != mint(0)) {
        mint rev = mint(1) / (*this)[i];
        FPS ret = (((*this * rev) >> i).log(deg) * k).exp(deg);
        ret *= (*this)[i].pow(k);
        ret = (ret << (i * k)).pre(deg);
        if ((int)ret.size() < deg) ret.resize(deg, mint(0));
        return ret;
      }
      if (__int128_t(i + 1) * k >= deg) return FPS(deg, mint(0));
    }
    return FPS(deg, mint(0));
  }

  static void *ntt_ptr;
  static void set_fft();
  FPS &operator*=(const FPS &r);
  void ntt();
  void intt();
  void ntt_doubling();
  static int ntt_pr();
  FPS inv(int deg = -1) const;
  FPS exp(int deg = -1) const;
};
template <typename mint>
void *FormalPowerSeries<mint>::ntt_ptr = nullptr;

/**
 * @brief 多項式/形式的冪級数ライブラリ
 * @docs docs/fps/formal-power-series.md
 */
#line 8 "fps/sparse-fps.hpp"

// g が sparse を仮定, f * g.inv() を計算
template <typename mint>
FormalPowerSeries<mint> sparse_div(const FormalPowerSeries<mint>& f,
                                   const FormalPowerSeries<mint>& g,
                                   int deg = -1) {
  assert(g.empty() == false && g[0] != mint(0));
  if (deg == -1) deg = f.size();
  mint ig0 = g[0].inverse();
  FormalPowerSeries<mint> s = f * ig0;
  s.resize(deg);
  vector<pair<int, mint>> gs;
  for (int i = 1; i < (int)g.size(); i++) {
    if (g[i] != 0) gs.emplace_back(i, g[i] * ig0);
  }
  for (int i = 0; i < deg; i++) {
    for (auto& [j, g_j] : gs) {
      if (i + j >= deg) break;
      s[i + j] -= s[i] * g_j;
    }
  }
  return s;
}

template <typename mint>
FormalPowerSeries<mint> sparse_inv(const FormalPowerSeries<mint>& f,
                                   int deg = -1) {
  assert(f.empty() == false && f[0] != mint(0));
  if (deg == -1) deg = f.size();
  vector<pair<int, mint>> fs;
  for (int i = 1; i < (int)f.size(); i++) {
    if (f[i] != 0) fs.emplace_back(i, f[i]);
  }
  FormalPowerSeries<mint> g(deg);
  mint if0 = f[0].inverse();
  if (0 < deg) g[0] = if0;
  for (int k = 1; k < deg; k++) {
    for (auto& [j, fj] : fs) {
      if (k < j) break;
      g[k] += g[k - j] * fj;
    }
    g[k] *= -if0;
  }
  return g;
}

template <typename mint>
FormalPowerSeries<mint> sparse_log(const FormalPowerSeries<mint>& f,
                                   int deg = -1) {
  assert(f.empty() == false && f[0] == 1);
  if (deg == -1) deg = f.size();
  vector<pair<int, mint>> fs;
  for (int i = 1; i < (int)f.size(); i++) {
    if (f[i] != 0) fs.emplace_back(i, f[i]);
  }

  int mod = mint::get_mod();
  static vector<mint> invs{1, 1};
  while ((int)invs.size() <= deg) {
    int i = invs.size();
    invs.push_back((-invs[mod % i]) * (mod / i));
  }

  FormalPowerSeries<mint> g(deg);
  for (int k = 0; k < deg - 1; k++) {
    for (auto& [j, fj] : fs) {
      if (k < j) break;
      int i = k - j;
      g[k + 1] -= g[i + 1] * fj * (i + 1);
    }
    g[k + 1] *= invs[k + 1];
    if (k + 1 < (int)f.size()) g[k + 1] += f[k + 1];
  }
  return g;
}

template <typename mint>
FormalPowerSeries<mint> sparse_exp(const FormalPowerSeries<mint>& f,
                                   int deg = -1) {
  assert(f.empty() or f[0] == 0);
  if (deg == -1) deg = f.size();
  vector<pair<int, mint>> fs;
  for (int i = 1; i < (int)f.size(); i++) {
    if (f[i] != 0) fs.emplace_back(i, f[i]);
  }

  int mod = mint::get_mod();
  static vector<mint> invs{1, 1};
  while ((int)invs.size() <= deg) {
    int i = invs.size();
    invs.push_back((-invs[mod % i]) * (mod / i));
  }

  FormalPowerSeries<mint> g(deg);
  if (deg) g[0] = 1;
  for (int k = 0; k < deg - 1; k++) {
    for (auto& [ip1, fip1] : fs) {
      int i = ip1 - 1;
      if (k < i) break;
      g[k + 1] += fip1 * g[k - i] * (i + 1);
    }
    g[k + 1] *= invs[k + 1];
  }
  return g;
}

template <typename mint>
FormalPowerSeries<mint> sparse_pow(const FormalPowerSeries<mint>& f,
                                   long long k, int deg = -1) {
  if (deg == -1) deg = f.size();
  if (k == 0) {
    FormalPowerSeries<mint> g(deg);
    if (deg) g[0] = 1;
    return g;
  }
  int zero = 0;
  while (zero != (int)f.size() and f[zero] == 0) zero++;
  if (zero == (int)f.size() or __int128_t(zero) * k >= deg) {
    return FormalPowerSeries<mint>(deg, 0);
  }
  if (zero != 0) {
    FormalPowerSeries<mint> suf{begin(f) + zero, end(f)};
    auto g = sparse_pow(suf, k, deg - zero * k);
    FormalPowerSeries<mint> h(zero * k, 0);
    copy(begin(g), end(g), back_inserter(h));
    return h;
  }

  auto mod = mint::get_mod();
  static vector<mint> invs{1, 1};
  while ((int)invs.size() <= deg) {
    int i = invs.size();
    invs.push_back((-invs[mod % i]) * (mod / i));
  }

  vector<pair<int, mint>> fs;
  for (int i = 1; i < (int)f.size(); i++) {
    if (f[i] != 0) fs.emplace_back(i, f[i]);
  }

  FormalPowerSeries<mint> g(deg);
  g[0] = f[0].pow(k);
  mint denom = f[0].inverse();
  k %= mint::get_mod();
  for (int a = 1; a < deg; a++) {
    for (auto& [i, f_i] : fs) {
      if (a < i) break;
      g[a] += f_i * g[a - i] * ((k + 1) * i - a);
    }
    g[a] *= denom * invs[a];
  }
  return g;
}

/**
 * @brief sparse な形式的冪級数の演算
 */


static const int M=55440;

int main()
{
  	ios::sync_with_stdio(false);
	cin.tie(nullptr);
	int K,N;
	cin>>K>>N;
	int mx=N;
	while(mx==13||mx==17||mx==19||mx==23)mx--;
	int mn=M/mx;
	int D=M-K*mn;
	ll ans=(K==13||K==17||K==19||K==23);
	if(D>=0){
		FormalPowerSeries<modint_2_61m1> P(D+1);
		rep(n,1,N+1){
			if(n==13||n==17||n==19||n==23)continue;
			int i=M/n-mn;
			if(i<=D)P[i]=1;
		}
		FormalPowerSeries<modint_2_61m1> Q=sparse_pow(P,K,D+1);
		ans+=Q[D].get();
	}
	cout<<ans<<'\n';
}