#432996 (C++17) No.997 Jumping Kangaroo

• 問題: No.997 Jumping Kangaroo
• ユーザー: Haar
• 提出日時: 2020-02-21 22:45:57
• 言語: C++17 (gcc 13.3.0 + boost 1.87.0)
• 結果: AC
• 実行時間: 3 ms / 2,000 ms
• コード長: 6,992 bytes
• コンパイル時間: 2,281 ms
• コンパイル使用メモリ: 199,736 KB
• 最終ジャッジ日時: 2025-01-09 01:40:32
• ジャッジサーバーID （参考情報）: judge1 / judge4

ファイルパターン	結果
sample	AC * 3
other	AC * 25

ソースコード

#include <bits/stdc++.h>
#define LLI long long int
#define FOR(v, a, b) for(LLI v = (a); v < (b); ++v)
#define FORE(v, a, b) for(LLI v = (a); v <= (b); ++v)
#define REP(v, n) FOR(v, 0, n)
#define REPE(v, n) FORE(v, 0, n)
#define REV(v, a, b) for(LLI v = (a); v >= (b); --v)
#define ALL(x) (x).begin(), (x).end()
#define RALL(x) (x).rbegin(), (x).rend()
#define ITR(it, c) for(auto it = (c).begin(); it != (c).end(); ++it)
#define RITR(it, c) for(auto it = (c).rbegin(); it != (c).rend(); ++it)
#define EXIST(c,x) ((c).find(x) != (c).end())
#define fst first
#define snd second
#define popcount __builtin_popcount
#define UNIQ(v) (v).erase(unique(ALL(v)), (v).end())
#define bit(i) (1LL<<(i))

#ifdef DEBUG
#include <Mylib/Debug/debug.cpp>
#else
#define dump(...) ((void)0)
#endif

using namespace std;

template <typename I> void join(ostream &ost, I s, I t, string d=" "){for(auto i=s; i!=t; ++i){if(i!=s)ost<<d; ost<<*i;}ost<<endl;}
template <typename T> istream& operator>>(istream &is, vector<T> &v){for(auto &a : v) is >> a; return is;}
template <typename T> void puts_all(const T &value){std::cout << value << "\n";}
template <typename T, typename ...Args> void puts_all(const T &value, const Args&... args){std::cout << value << " ";puts_all(args...);}

template <typename T, typename U> bool chmin(T &a, const U &b){return (a>b ? a=b, true : false);}
template <typename T, typename U> bool chmax(T &a, const U &b){return (a<b ? a=b, true : false);}
template <typename T, size_t N, typename U> void fill_array(T (&a)[N], const U &v){fill((U*)a, (U*)(a+N), v);}
template <typename T> auto make_vector(int n, int m, const T &value){return vector<vector<T>>(n, vector<T>(m, value));}


struct Init{
  Init(){
    cin.tie(0);
    ios::sync_with_stdio(false);
    cout << fixed << setprecision(12);
    cerr << fixed << setprecision(12);
  }
}init;


template <uint32_t M> class ModInt{
public:
  uint64_t val;
  
  constexpr ModInt(): val(0){}
  constexpr ModInt(std::int64_t n){
    if(n >= M) val = n % M;
    else if(n < 0) val = n % M + M;
    else val = n;
  }
  
  inline constexpr auto operator+(const ModInt &a) const {return ModInt(val + a.val);}
  inline constexpr auto operator-(const ModInt &a) const {return ModInt(val - a.val);}
  inline constexpr auto operator*(const ModInt &a) const {return ModInt(val * a.val);}
  inline constexpr auto operator/(const ModInt &a) const {return ModInt(val * a.inv().val);}
  
  inline constexpr auto& operator=(const ModInt &a){val = a.val; return *this;}
  inline constexpr auto& operator+=(const ModInt &a){if((val += a.val) >= M) val -= M; return *this;}
  inline constexpr auto& operator-=(const ModInt &a){if(val < a.val) val += M; val -= a.val; return *this;}
  inline constexpr auto& operator*=(const ModInt &a){(val *= a.val) %= M; return *this;}
  inline constexpr auto& operator/=(const ModInt &a){(val *= a.inv().val) %= M; return *this;}
 
  inline constexpr bool operator==(const ModInt &a) const {return val == a.val;}
  inline constexpr bool operator!=(const ModInt &a) const {return val != a.val;}
 
  inline constexpr auto& operator++(){*this += 1; return *this;}
  inline constexpr auto& operator--(){*this -= 1; return *this;}
 
  inline constexpr auto operator++(int){auto t = *this; *this += 1; return t;}
  inline constexpr auto operator--(int){auto t = *this; *this -= 1; return t;}
 
  inline constexpr static ModInt power(int64_t n, int64_t p){
    if(p < 0) return power(n, -p).inv();
    
    int64_t ret = 1, e = n;
    for(; p; (e *= e) %= M, p >>= 1) if(p & 1) (ret *= e) %= M;
    return ret;
  }
 
  inline constexpr static ModInt inv(int64_t a){
    int64_t b = M, u = 1, v = 0;
    
    while(b){
      int64_t t = a / b;
      a -= t * b; std::swap(a,b);
      u -= t * v; std::swap(u,v);
    }
 
    u %= M;
    if(u < 0) u += M;
    
    return u;
  }
 
  inline constexpr static auto frac(int64_t a, int64_t b){return ModInt(a) / ModInt(b);}
  
  inline constexpr auto power(int64_t p) const {return power(val, p);}
  inline constexpr auto inv() const {return inv(val);}
 
  friend inline constexpr auto operator-(const ModInt &a){return ModInt(-a.val);}
 
  friend inline constexpr auto operator+(int64_t a, const ModInt &b){return ModInt(a) + b;}
  friend inline constexpr auto operator-(int64_t a, const ModInt &b){return ModInt(a) - b;}
  friend inline constexpr auto operator*(int64_t a, const ModInt &b){return ModInt(a) * b;}
  friend inline constexpr auto operator/(int64_t a, const ModInt &b){return ModInt(a) / b;}
 
  friend std::istream& operator>>(std::istream &s, ModInt<M> &a){s >> a.val; return s;}
  friend std::ostream& operator<<(std::ostream &s, const ModInt<M> &a){s << a.val; return s;}
};


template <typename T, int N> struct SquareMatrix{
  std::array<std::array<T,N>,N> matrix;

  SquareMatrix(){for(size_t i = 0; i < N; ++i) for(size_t j = 0; j < N; ++j) matrix[i][j] = 0;}
  SquareMatrix(std::initializer_list<std::initializer_list<T>> list){
    int i = 0;
    for(auto it1 = list.begin(); it1 != list.end(); ++it1, ++i){
      int j = 0;
      for(auto it2 = it1->begin(); it2 != it1->end(); ++it2, ++j){
        matrix[i][j] = *it2;
      }
    }
  }

  bool operator==(const SquareMatrix &val) const {return matrix == val.matrix;}
  bool operator!=(const SquareMatrix &val) const {return !(*this == val);}
  auto& operator=(const SquareMatrix &val){this->matrix = val.matrix; return *this;}

  auto& operator*=(const SquareMatrix &val){
    std::array<std::array<T,N>,N> temp;
    for(size_t i = 0; i < N; ++i) for(size_t j = 0; j < N; ++j) for(size_t k = 0; k < N; ++k) temp[i][j] += matrix[i][k] * val[k][j];
    std::swap(matrix, temp);
    return *this;
  }

  friend auto operator*(const SquareMatrix &a, const SquareMatrix &b){auto ret = a; ret *= b; return ret;}

  inline const auto& operator[](size_t i) const {return matrix[i];}
  inline auto& operator[](size_t i){return matrix[i];}
  inline int size() const {return N;}
  
  static auto make_unit(){SquareMatrix ret; for(size_t i = 0; i < N; ++i) ret[i][i] = 1; return ret;}
};

template <typename T, int N> SquareMatrix<T,N> power(SquareMatrix<T,N> a, uint64_t p){
  if(p == 0) return SquareMatrix<T,N>::make_unit();
  if(p == 1) return a;
  
  auto temp = power(a, p/2);
  auto ret = temp * temp;

  if(p%2) ret *= a;
 
  return ret;
}

using mint = ModInt<1000000007>;
using Mat = SquareMatrix<mint, 2>;


int main(){
  LLI N, W, K; cin >> N >> W >> K;
  vector<int> A(N); cin >> A;

  mint x = 0, y = 0;

  {
    auto dp1 = vector<mint>(W+1, 0);
    dp1[0] = 1;
    FORE(i,0,W){
      for(auto &d : A){
        if(i+d <= W) dp1[i+d] += dp1[i];
      }
    }

    x = dp1[W];

    auto dp2 = vector<mint>(2*W+1, 0);
    dp2[0] = 1;
    FORE(i,0,2*W){
      for(auto &d : A){
        if(i+d <= 2*W and i+d != W) dp2[i+d] += dp2[i];
      }
    }

    y = dp2[2*W];
  }

  dump(x, y);

  Mat m = {{x, y}, {1, 0}};
  m = power(m, K-1);

  mint ans = m[0][0] * x + m[0][1];

  puts_all(ans);


  return 0;
}