#479610 (C++17) No.1050 Zero (Maximum)

• 問題: No.1050 Zero (Maximum)
• ユーザー: tanimani364
• 提出日時: 2020-05-09 11:45:33
• 言語: C++17 (gcc 12.3.0 + boost 1.83.0)
• 結果: AC
• 実行時間: 25 ms / 2,000 ms
• コード長: 5,842 bytes
• コンパイル時間: 2,430 ms
• コンパイル使用メモリ: 209,720 KB
• 実行使用メモリ: 5,376 KB
• 最終ジャッジ日時: 2024-07-05 15:42:42
• 合計ジャッジ時間: 3,235 ms
• ジャッジサーバーID （参考情報）: judge5 / judge3

入力	結果	実行時間; 実行使用メモリ
testcase_00	AC	2 ms; 5,248 KB
testcase_01	AC	2 ms; 5,376 KB
testcase_02	AC	8 ms; 5,376 KB
testcase_03	AC	5 ms; 5,376 KB
testcase_04	AC	16 ms; 5,376 KB
testcase_05	AC	17 ms; 5,376 KB
testcase_06	AC	8 ms; 5,376 KB
testcase_07	AC	10 ms; 5,376 KB
testcase_08	AC	3 ms; 5,376 KB
testcase_09	AC	5 ms; 5,376 KB
testcase_10	AC	21 ms; 5,376 KB
testcase_11	AC	15 ms; 5,376 KB
testcase_12	AC	2 ms; 5,376 KB
testcase_13	AC	2 ms; 5,376 KB
testcase_14	AC	2 ms; 5,376 KB
testcase_15	AC	2 ms; 5,376 KB
testcase_16	AC	23 ms; 5,376 KB
testcase_17	AC	25 ms; 5,376 KB

ソースコード

#include<bits/stdc++.h>
#define rep(i,a) for(int i=(int)0;i<(int)a;++i)
#define rrep(i,a) for(int i=(int)a-1;i>=0;--i)
#define REP(i,a,b) for(int i=(int)a;i<(int)b;++i)
#define RREP(i,a,b) for(int i=(int)a-1;i>=b;--i)
#define pb push_back
#define eb emplace_back
#define all(x) x.begin(),x.end()
#define rall(x) x.rbegin(),x.rend()
using ll=long long;
constexpr ll mod = 1e9 + 7;
constexpr ll INF = 1LL << 60;
 
template<class T> inline bool chmin(T& a, T b) {
    if (a > b) {
        a = b;
        return true;
    }
    return false;
}
template<class T> inline bool chmax(T& a, T b) {
    if (a < b) {
        a = b;
        return true;
    }
    return false;
}


ll gcd(ll n, ll m) {
    ll tmp;
    while (m!=0) {
        tmp = n % m;
        n = m;
        m = tmp;
    }
    return n;
}
 
ll lcm(ll n, ll m) {
    return abs(n) / gcd(n, m)*abs(m);//gl=xy
}

using namespace std;

template< int mod >
struct ModInt {
  int x;

  ModInt() : x(0) {}

  ModInt(int64_t y) : x(y >= 0 ? y % mod : (mod - (-y) % mod) % mod) {}

  ModInt &operator+=(const ModInt &p) {
    if((x += p.x) >= mod) x -= mod;
    return *this;
  }

  ModInt &operator-=(const ModInt &p) {
    if((x += mod - p.x) >= mod) x -= mod;
    return *this;
  }

  ModInt &operator*=(const ModInt &p) {
    x = (int) (1LL * x * p.x % mod);
    return *this;
  }

  ModInt &operator/=(const ModInt &p) {
    *this *= p.inverse();
    return *this;
  }

  ModInt operator-() const { return ModInt(-x); }

  ModInt operator+(const ModInt &p) const { return ModInt(*this) += p; }

  ModInt operator-(const ModInt &p) const { return ModInt(*this) -= p; }

  ModInt operator*(const ModInt &p) const { return ModInt(*this) *= p; }

  ModInt operator/(const ModInt &p) const { return ModInt(*this) /= p; }

  bool operator==(const ModInt &p) const { return x == p.x; }

  bool operator!=(const ModInt &p) const { return x != p.x; }

  ModInt inverse() const {
    int a = x, b = mod, u = 1, v = 0, t;
    while(b > 0) {
      t = a / b;
      swap(a -= t * b, b);
      swap(u -= t * v, v);
    }
    return ModInt(u);
  }

  ModInt pow(int64_t n) const {
    ModInt ret(1), mul(x);
    while(n > 0) {
      if(n & 1) ret *= mul;
      mul *= mul;
      n >>= 1;
    }
    return ret;
  }

  friend ostream &operator<<(ostream &os, const ModInt &p) {
    return os << p.x;
  }

  friend istream &operator>>(istream &is, ModInt &a) {
    int64_t t;
    is >> t;
    a = ModInt< mod >(t);
    return (is);
  }

  static int get_mod() { return mod; }
};

using modint = ModInt< mod >;

template< class T >
struct Matrix {
  vector< vector< T > > A;

  Matrix() {}

  Matrix(size_t n, size_t m) : A(n, vector< T >(m, 0)) {}

  Matrix(size_t n) : A(n, vector< T >(n, 0)) {};

  size_t height() const {
    return (A.size());
  }

  size_t width() const {
    return (A[0].size());
  }

  inline const vector< T > &operator[](int k) const {
    return (A.at(k));
  }

  inline vector< T > &operator[](int k) {
    return (A.at(k));
  }

  static Matrix I(size_t n) {
    Matrix mat(n);
    for(int i = 0; i < n; i++) mat[i][i] = 1;
    return (mat);
  }

  Matrix &operator+=(const Matrix &B) {
    size_t n = height(), m = width();
    assert(n == B.height() && m == B.width());
    for(int i = 0; i < n; i++)
      for(int j = 0; j < m; j++)
        (*this)[i][j] += B[i][j];
    return (*this);
  }

  Matrix &operator-=(const Matrix &B) {
    size_t n = height(), m = width();
    assert(n == B.height() && m == B.width());
    for(int i = 0; i < n; i++)
      for(int j = 0; j < m; j++)
        (*this)[i][j] -= B[i][j];
    return (*this);
  }

  Matrix &operator*=(const Matrix &B) {
    size_t n = height(), m = B.width(), p = width();
    assert(p == B.height());
    vector< vector< T > > C(n, vector< T >(m, 0));
    for(int i = 0; i < n; i++)
      for(int j = 0; j < m; j++)
        for(int k = 0; k < p; k++)
          C[i][j] = (C[i][j] + (*this)[i][k] * B[k][j]);
    A.swap(C);
    return (*this);
  }

  Matrix &operator^=(long long k) {
    Matrix B = Matrix::I(height());
    while(k > 0) {
      if(k & 1) B *= *this;
      *this *= *this;
      k >>= 1LL;
    }
    A.swap(B.A);
    return (*this);
  }

  Matrix operator+(const Matrix &B) const {
    return (Matrix(*this) += B);
  }

  Matrix operator-(const Matrix &B) const {
    return (Matrix(*this) -= B);
  }

  Matrix operator*(const Matrix &B) const {
    return (Matrix(*this) *= B);
  }

  Matrix operator^(const long long k) const {
    return (Matrix(*this) ^= k);
  }

  friend ostream &operator<<(ostream &os, Matrix &p) {
    size_t n = p.height(), m = p.width();
    for(int i = 0; i < n; i++) {
      os << "[";
      for(int j = 0; j < m; j++) {
        os << p[i][j] << (j + 1 == m ? "]\n" : ",");
      }
    }
    return (os);
  }


  T determinant() {
    Matrix B(*this);
    assert(width() == height());
    T ret = 1;
    for(int i = 0; i < width(); i++) {
      int idx = -1;
      for(int j = i; j < width(); j++) {
        if(B[j][i] != 0) idx = j;
      }
      if(idx == -1) return (0);
      if(i != idx) {
        ret *= -1;
        swap(B[i], B[idx]);
      }
      ret *= B[i][i];
      T vv = B[i][i];
      for(int j = 0; j < width(); j++) {
        B[i][j] /= vv;
      }
      for(int j = i + 1; j < width(); j++) {
        T a = B[j][i];
        for(int k = 0; k < width(); k++) {
          B[j][k] -= B[i][k] * a;
        }
      }
    }
    return (ret);
  }
};

void solve()
{
  ll m, k;
  cin >> m >> k;
  Matrix<modint> mat(m, m),mat2(m,m);
  mat2[0][0] = 1;
  rep(i, m)
  {
    rep(j,m){
      mat[i][(i + j) % m] += 1;
      mat[i][(i * j) % m] += 1;
    }
  }
  mat ^= k;
  Matrix<modint> ans = mat * mat2;
  cout << ans[0][0] << "\n";
}

int main(){
    ios::sync_with_stdio(false);
    cin.tie(0);
    cout<<fixed<<setprecision(15);
    solve();
    return 0;
}