結果

問題 No.214 素数サイコロと合成数サイコロ (3-Medium)
コンテスト
ユーザー fumiphys
提出日時 2019-10-05 20:36:07
言語 C++14
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 1,314 ms / 3,000 ms
コード長 5,540 bytes
コンパイル時間 1,961 ms
コンパイル使用メモリ 175,580 KB
実行使用メモリ 9,728 KB
最終ジャッジ日時 2024-10-07 00:56:02
合計ジャッジ時間 7,275 ms
ジャッジサーバーID
（参考情報） 		judge2 / judge1
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ファイルパターン 結果
other AC * 3
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ソースコード

diff # 

// includes
#include <bits/stdc++.h>
using namespace std;

// macros
#define pb emplace_back
#define mk make_pair
#define FOR(i, a, b) for(int i=(a);i<(b);++i)
#define rep(i, n) FOR(i, 0, n)
#define rrep(i, n) for(int i=((int)(n)-1);i>=0;i--)
#define irep(itr, st) for(auto itr = (st).begin(); itr != (st).end(); ++itr)
#define irrep(itr, st) for(auto itr = (st).rbegin(); itr != (st).rend(); ++itr)
#define all(x) (x).begin(),(x).end()
#define sz(x) ((int)(x).size())
#define UNIQUE(v) v.erase(unique(v.begin(), v.end()), v.end())
#define bit(n) (1LL<<(n))
// functions
template <class T>bool chmax(T &a, const T &b){if(a < b){a = b; return 1;} return 0;}
template <class T>bool chmin(T &a, const T &b){if(a > b){a = b; return 1;} return 0;}
template <typename T> istream &operator>>(istream &is, vector<T> &vec){for(auto &v: vec)is >> v; return is;}
template <typename T> ostream &operator<<(ostream &os, const vector<T>& vec){for(int i = 0; i < vec.size(); i++){ os << vec[i]; if(i + 1 != vec.size())os << " ";} return os;}
template <typename T> ostream &operator<<(ostream &os, const set<T>& st){for(auto itr = st.begin(); itr != st.end(); ++itr){ os << *itr; auto titr = itr; if(++titr != st.end())os << " ";} return os;}
template <typename T> ostream &operator<<(ostream &os, const unordered_set<T>& st){for(auto itr = st.begin(); itr != st.end(); ++itr){ os << *itr; auto titr = itr; if(++titr != st.end())os << " ";} return os;}
template <typename T> ostream &operator<<(ostream &os, const multiset<T>& st){for(auto itr = st.begin(); itr != st.end(); ++itr){ os << *itr; auto titr = itr; if(++titr != st.end())os << " ";} return os;}
template <typename T> ostream &operator<<(ostream &os, const unordered_multiset<T>& st){for(auto itr = st.begin(); itr != st.end(); ++itr){ os << *itr; auto titr = itr; if(++titr != st.end())os << " ";} return os;}
template <typename T1, typename T2> ostream &operator<<(ostream &os, const pair<T1, T2> &p){os << p.first << " " << p.second; return os;}
template <typename T1, typename T2> ostream &operator<<(ostream &os, const map<T1, T2> &mp){for(auto itr = mp.begin(); itr != mp.end(); ++itr){ os << itr->first << ":" << itr->second; auto titr = itr; if(++titr != mp.end())os << " "; } return os;}
template <typename T1, typename T2> ostream &operator<<(ostream &os, const unordered_map<T1, T2> &mp){for(auto itr = mp.begin(); itr != mp.end(); ++itr){ os << itr->first << ":" << itr->second; auto titr = itr; if(++titr != mp.end())os << " "; } return os;}
//  types
using ll = long long int;
using P = pair<int, int>;
// constants
const int inf = 1e9;
const ll linf = 1LL << 50;
const double EPS = 1e-10;
const int mod = 1000000007;
const int dx[4] = {-1, 0, 1, 0};
const int dy[4] = {0, -1, 0, 1};
// io
struct fast_io{
  fast_io(){ios_base::sync_with_stdio(false); cin.tie(0); cout << fixed << setprecision(20);}
} fast_io_;

const int MOD = mod;

struct Kitamasa{
  int k;
  vector<long long> a, d;
  Kitamasa(vector<long long> a, vector<long long> d): a(a), d(d){
    k = a.size();
  }
  vector<long long> mul(vector<long long> &x, vector<long long> &y){
    vector<long long> t(2 * k, 0);
    for(int i = 0; i < k; i++){
      for(int j = 0; j < k; j++){
        (t[i+j] += x[i] * y[j] % MOD) %= MOD;
      }
    }
    for(int i = 2*k-2; i >= k; i--){
      for(int j = 1; j <= k; j++){
        (t[i-j] += d[k-j] * t[i] % MOD) %= MOD;
      }
    }
    t.resize(k);
    return t;
  }
  vector<long long> calc_coeff(long long n){
    vector<long long> p(k, 0), v(k, 0);
    p[0] = v[1] = 1;
    while(n){
      if(n % 2)p = mul(p, v);
      v = mul(v, v);
      n /= 2;
    }
    return p;
  }
  long long calc(long long n){
    vector<long long> c = calc_coeff(n);
    long long res = 0;
    for(int i = 0; i < k; i++)res = (res + a[i] * c[i] % MOD) % MOD;
    return res;
  }
};

int a[6] = {2, 3, 5, 7, 11, 13};
int b[6] = {4, 6, 8, 9, 10, 12};
ll d1[1301], d2[1301], nex[1301];
ll dp1[7][51][1301], dp2[7][51][1301];
ll C[1301], CS[1301];

int main(int argc, char const* argv[])
{
  ll n;
  int p, c;
  cin >> n >> p >> c;

  dp1[0][0][0] = 1;
  rep(i, 6){
    rep(j, p + 1){
      rep(k, 1301){
        rep(l, j + 1){
          if(k-l*a[i]>=0)(dp1[i+1][j][k] += dp1[i][j-l][k-l*a[i]]) %= mod;
        }
      }
    }
  }
  dp2[0][0][0] = 1;
  rep(i, 6){
    rep(j, c + 1){
      rep(k, 1301){
        rep(l, j + 1){
          if(k-l*b[i]>=0)(dp2[i+1][j][k] += dp2[i][j-l][k-l*b[i]]) %= mod;
        }
      }
    }
  }
  rep(i, 1301)d1[i] = dp1[6][p][i];
  rep(i, 1301)d2[i] = dp2[6][c][i];

  FOR(i, 1, 1301){
    rep(j, i + 1){
      (C[i] += d1[j] * d2[i-j] % mod) %= mod;
    }
  }
  rrep(i, 1301){
    CS[i] = (C[i] + (i < 1300 ? CS[i+1]: 0)) % mod;
  }
  vector<ll> A(2601, 0); A[0] = 1;
  vector<ll> B(1300); rep(i, 1300)B[i] = C[1300-i];
  for(int i = 1; i <= 2600; i++){
    for(int j = 1; j <= 1300; j++){
      if(i-j>=0)(A[i] += A[i-j] * C[j] % mod) %= mod;
    }
  }
  if(n <= 1300){
    ll res = A[n];
    for(int i = 1; i <= 1300; i++){
      if(n - i < 0)continue;
      ll tmp = A[n-i] * CS[i+1] % mod;
      res = (res + tmp) % mod;
    }
    cout << res << endl;
  }else{
    vector<ll> D = A; D.resize(1300);
    Kitamasa kt(D, B);
    vector<ll> co = kt.calc_coeff(n - 1299);
    ll res = 0;
    for(ll i = n - 1299; i <= n; ++i){
      ll ai = 0;
      rep(j, 1300)ai = (ai + co[j] * A[j+i-n+1299] % mod) % mod;
      if(i < n){
        res = (res + ai * CS[n-i+1] % mod) % mod;
      }else res = (res + ai) % mod;
    }
    cout << res << endl;
  }
  return 0;
}
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