結果

問題 No.42 貯金箱の溜息
コンテスト
ユーザー fumiphys
提出日時 2020-04-11 00:02:45
言語 C++14
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 42 ms / 5,000 ms
コード長 6,384 bytes
コンパイル時間 1,866 ms
コンパイル使用メモリ 176,108 KB
実行使用メモリ 5,376 KB
最終ジャッジ日時 2024-09-16 03:54:30
合計ジャッジ時間 2,220 ms
ジャッジサーバーID
（参考情報） 		judge5 / 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 whole(x) (x).begin(),(x).end()
#define sz(x) ((int)(x).size())
#define bit(n) (1LL<<(n))
// functions
template <typename T> void unique(T& c){c.erase(std::unique(c.begin(), c.end()), c.end());}
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 = 1000000009;
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(nullptr); cout << fixed << setprecision(20);}
} fast_io_;

template<typename T>
T extgcd(T a, T b, T &x, T &y){ 
  T d = a;
  if(b != 0){
    d = extgcd(b, a % b, y, x);
    y -= (a / b) * x;
  }else{
    x = 1, y = 0;
  }
  return d;
}

template <typename T>
T modinv(T a, T m){
  long long x = 0, y = 0;
  extgcd<long long>(a, m, x, y);
  x %= m;
  if(x < 0)x += m;
  return x;
}

template <typename T>
T power(T a, T n, T mod) {
  T res = 1;
  T tmp = n;
  T curr = a;
  while(tmp){
    if(tmp % 2 == 1){
      res = (T)(res * curr % mod);
    }
    curr = (T)(curr * curr % mod);
    tmp >>= 1;
  }

  return res;
}

struct Mint{
  const static ll default_mod = (ll)(1e9 + 9);
  ll MOD = default_mod;
  ll x = 0;
  ll get_mod(){
    return MOD;
  }
  Mint(){}
  Mint(ll x_, ll MOD=default_mod): MOD(MOD){
    x = x_;
    x %= MOD;
    if(x < 0)x += MOD;
  }
  Mint(const Mint &m){
    x = m.x;
    MOD = m.MOD;
  }
  Mint &operator+=(const Mint &y){
    x = (x + y.x) % MOD;
    if(x < 0)x += MOD;
    return *this;
  }
  Mint &operator-=(const Mint &y){
    x = (x - y.x) % MOD;
    if(x < 0)x += MOD;
    return *this;
  }
  Mint &operator*=(const Mint &y){
    x = (x * y.x) % MOD;
    if(x < 0)x += MOD;
    return *this;
  }
  Mint inverse() const{
    return Mint(modinv<ll>(x, MOD), MOD);
  }
  Mint &operator/=(const Mint &y){
    x = (x * y.inverse().x) % MOD;
    if(x < 0)x += MOD;
    return *this;
  }
  Mint operator-() const{
    return Mint(-x, MOD);
  }
  Mint operator+(const Mint &y) const{
    return Mint(*this) += y;
  }
  Mint operator-(const Mint &y) const{
    return Mint(*this) -= y;
  }
  Mint operator*(const Mint &y) const{
    return Mint(*this) *= y;
  }
  Mint operator/(const Mint &y) const{
    return Mint(*this) /= y;
  }
  bool operator==(const Mint &y) const{
    return x == y.x;
  }
  bool operator!=(const Mint &y) const{
    return x != y.x;
  }
  Mint pow(long long k) const{
    long long ret = power<long long>(x, k, MOD);
    return Mint(ret, MOD);
  }
  friend ostream& operator<<(ostream &os, const Mint &m){
    return os << m.x;
  }
  friend istream& operator>>(istream &is, Mint &m){
    ll t;
    is >> t;
    m = Mint(t);
    return is;
  }
  explicit operator long long() const{
    return x;
  }
};


template <typename T>
struct LagrangeInterpolationM{
  int n = 0;
  vector<T> x, y;
  vector<T> nume;
  LagrangeInterpolationM(){}
  LagrangeInterpolationM(const vector<T> &x, const vector<T> &y): x(x), y(y){
    n = x.size() - 1;
    nume.resize(n + 1);
    for(int i = 0; i <= n; i++){
      T t = T(1);
      for(int j = 0; j <= n; j++){
        if(i == j)continue;
        t = t * (x[i] - x[j]);
      }
      nume[i] = t.inverse();
    }
  }
  T val(T t){
    T a = T(1);
    for(int i = 0; i <= n; i++){
      if(t == x[i])return y[i];
      a = a * (t - x[i]);
    }
    T res = T(0);
    for(int i = 0; i <= n; i++){
      res += y[i] * nume[i] * (a / (t - x[i]));
    }
    return res;
  }
};

int d[6] = {1, 5, 10, 50, 100, 500};
ll dp[10010];

int main(int argc, char const* argv[])
{
  dp[0] = 1;
  rep(i, 6){
    rep(j, 10010){
      if(j-d[i]>=0)(dp[j] += dp[j-d[i]]) %= mod;
    }
  }
  vector<LagrangeInterpolationM<Mint>> rip(500);
  rep(i, 500){
    vector<Mint> x(7), y(7);
    rep(j, 7){
      x[j] = j;
      y[j] = dp[i + 500 * j];
    }
    rip[i] = LagrangeInterpolationM<Mint>(x, y);
  }
  int t; cin >> t;
  rep(i_, t){
    ll m; cin >> m;
    cout << rip[m%500].val(m/500) << endl;
  }
  return 0;
}
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