#473203 (C++14) No.1050 Zero (Maximum)

• 問題: No.1050 Zero (Maximum)
• ユーザー: stoq
• 提出日時: 2020-05-01 07:39:59
• 言語: C++14 (gcc 12.3.0 + boost 1.83.0)
• 結果: AC
• 実行時間: 21 ms / 2,000 ms
• コード長: 6,931 bytes
• コンパイル時間: 1,594 ms
• コンパイル使用メモリ: 182,812 KB
• 実行使用メモリ: 5,376 KB
• 最終ジャッジ日時: 2024-06-02 12:26:30
• 合計ジャッジ時間: 2,428 ms
• ジャッジサーバーID （参考情報）: judge5 / judge1

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	1 ms; 5,376 KB
testcase_02	AC	7 ms; 5,376 KB
testcase_03	AC	4 ms; 5,376 KB
testcase_04	AC	13 ms; 5,376 KB
testcase_05	AC	15 ms; 5,376 KB
testcase_06	AC	7 ms; 5,376 KB
testcase_07	AC	9 ms; 5,376 KB
testcase_08	AC	2 ms; 5,376 KB
testcase_09	AC	5 ms; 5,376 KB
testcase_10	AC	17 ms; 5,376 KB
testcase_11	AC	13 ms; 5,376 KB
testcase_12	AC	2 ms; 5,376 KB
testcase_13	AC	2 ms; 5,376 KB
testcase_14	AC	1 ms; 5,376 KB
testcase_15	AC	2 ms; 5,376 KB
testcase_16	AC	19 ms; 5,376 KB
testcase_17	AC	21 ms; 5,376 KB

ソースコード

#define MOD_TYPE 1

#pragma region Macros
#include <bits/stdc++.h>
using namespace std;
/*
#include <boost/multiprecision/cpp_int.hpp>
#include <boost/multiprecision/cpp_dec_float.hpp>
using multiInt = boost::multiprecision::cpp_int;
using lld = boost::multiprecision::cpp_dec_float_100;
*/
/*
#pragma GCC target("avx2")
#pragma GCC optimize("O3")
#pragma GCC optimize("unroll-loops")
*/
using ll = long long int;
using ld = long double;
using pii = pair<int, int>;
using pll = pair<ll, ll>;
using pld = pair<ld, ld>;
template <typename Q_type>
using smaller_queue = priority_queue<Q_type, vector<Q_type>, greater<Q_type>>;

constexpr ll MOD = (MOD_TYPE == 1 ? (ll)(1e9 + 7) : 998244353);
constexpr int INF = (int)1e9;
constexpr ll LINF = (ll)4e18;
constexpr ld PI = acos(-1.0);
constexpr ld EPS = 1e-11;
constexpr int Dx[] = {0, 0, -1, 1, -1, 1, -1, 1, 0};
constexpr int Dy[] = {1, -1, 0, 0, -1, -1, 1, 1, 0};

#define REP(i, m, n) for (ll i = m; i < (ll)(n); ++i)
#define rep(i, n) REP(i, 0, n)
#define REPI(i, m, n) for (int i = m; i < (int)(n); ++i)
#define repi(i, n) REPI(i, 0, n)
#define MP make_pair
#define MT make_tuple
#define YES(n) cout << ((n) ? "YES" : "NO") << "\n"
#define Yes(n) cout << ((n) ? "Yes" : "No") << "\n"
#define possible(n) cout << ((n) ? "possible" : "impossible") << "\n"
#define Possible(n) cout << ((n) ? "Possible" : "Impossible") << "\n"
#define Yay(n) cout << ((n) ? "Yay!" : ":(") << "\n"
#define all(v) v.begin(), v.end()
#define NP(v) next_permutation(all(v))
#define dbg(x) cerr << #x << ":" << x << "\n";

inline void init_main()
{
  cin.tie(0);
  ios::sync_with_stdio(false);
  cout << setprecision(30) << setiosflags(ios::fixed);
}
template <typename T>
inline bool chmin(T &a, T b)
{
  if (a > b)
  {
    a = b;
    return true;
  }
  return false;
}
template <typename T>
inline bool chmax(T &a, T b)
{
  if (a < b)
  {
    a = b;
    return true;
  }
  return false;
}
inline ll CEIL(ll a, ll b)
{
  return (a + b - 1) / b;
}
template <typename A, size_t N, typename T>
inline void Fill(A (&array)[N], const T &val)
{
  fill((T *)array, (T *)(array + N), val);
}
#pragma endregion

template <int MOD>
struct Fp
{
  long long val;

  constexpr Fp(long long v = 0) noexcept : val(v % MOD)
  {
    if (val < 0)
      v += MOD;
  }

  constexpr int getmod()
  {
    return MOD;
  }

  constexpr Fp operator-() const noexcept
  {
    return val ? MOD - val : 0;
  }

  constexpr Fp operator+(const Fp &r) const noexcept
  {
    return Fp(*this) += r;
  }

  constexpr Fp operator-(const Fp &r) const noexcept
  {
    return Fp(*this) -= r;
  }

  constexpr Fp operator*(const Fp &r) const noexcept
  {
    return Fp(*this) *= r;
  }

  constexpr Fp operator/(const Fp &r) const noexcept
  {
    return Fp(*this) /= r;
  }

  constexpr Fp &operator+=(const Fp &r) noexcept
  {
    val += r.val;
    if (val >= MOD)
      val -= MOD;
    return *this;
  }

  constexpr Fp &operator-=(const Fp &r) noexcept
  {
    val -= r.val;
    if (val < 0)
      val += MOD;
    return *this;
  }

  constexpr Fp &operator*=(const Fp &r) noexcept
  {
    val = val * r.val % MOD;
    return *this;
  }

  constexpr Fp &operator/=(const Fp &r) noexcept
  {
    long long a = r.val, b = MOD, u = 1, v = 0;
    while (b)
    {
      long long t = a / b;
      a -= t * b;
      swap(a, b);
      u -= t * v;
      swap(u, v);
    }
    val = val * u % MOD;
    if (val < 0)
      val += MOD;
    return *this;
  }

  constexpr bool operator==(const Fp &r) const noexcept
  {
    return this->val == r.val;
  }

  constexpr bool operator!=(const Fp &r) const noexcept
  {
    return this->val != r.val;
  }

  friend constexpr ostream &operator<<(ostream &os, const Fp<MOD> &x) noexcept
  {
    return os << x.val;
  }

  friend constexpr istream &operator>>(istream &is, Fp<MOD> &x) noexcept
  {
    return is >> x.val;
  }
};

Fp<MOD> modpow(const Fp<MOD> &a, long long n) noexcept
{
  if (n == 0)
    return 1;
  auto t = modpow(a, n / 2);
  t = t * t;
  if (n & 1)
    t = t * a;
  return t;
}

using mint = Fp<MOD>;

template <typename T>
class Matrix
{
public:
  size_t N, M;
  vector<vector<T>> data;

  Matrix(size_t N_, size_t M_) : N(N_), M(M_)
  {
    data.resize(N, vector<T>(M));
  }

  Matrix operator+(const Matrix &A)
  {
    assert(A.N == N && A.M == M);
    Matrix res(N, M);
    rep(i, N) rep(j, M) res[i][j] = data[i][j] + A[i][j];
    return res;
  }

  Matrix &operator+=(const Matrix &A)
  {
    assert(A.N == N && A.M == M);
    rep(i, N) rep(j, M) data[i][j] += A[i][j];
    return *this;
  }

  Matrix operator-(const Matrix &A)
  {
    assert(A.N == N && A.M == M);
    Matrix<T> res(N, M);
    rep(i, N) rep(j, M) res.data[i][j] = data[i][j] - A[i][j];
    return res;
  }

  Matrix &operator-=(const Matrix &A)
  {
    assert(A.N == N && A.M == M);
    rep(i, N) rep(j, M) data[i][j] -= A[i][j];
    return *this;
  }

  Matrix operator*(const Matrix &A)
  {
    assert(M == A.N);
    Matrix res(N, A.M);

    rep(i, N) rep(j, A.M)
    {
      rep(k, M) res[i][j] += data[i][k] * A[k][j];
    }
    return res;
  }

  Matrix &operator*=(const Matrix<T> &A)
  {
    return *this = *this * A;
  }

  Matrix operator*(T a)
  {
    Matrix res(N, M);
    rep(i, N) rep(j, M) res[i][j] = data[i][j] * a;
    return res;
  }

  Matrix &operator*=(ll a)
  {
    rep(i, N) rep(j, M) data[i][j] *= a;
    return *this;
  }

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

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

  bool operator==(Matrix &A)
  {
    if (N != A.N || M != A.M)
      return false;

    rep(i, N) rep(j, M)
    {
      if (data[i][j] != A[i][j])
        return false;
    }
    return true;
  }

  bool operator!=(Matrix &A)
  {
    return !(*this == A);
  }

  void display()
  {
    rep(i, N)
    {
      rep(j, M) cerr << data[i][j] << " ";
      cerr << endl;
    }
  }

  Matrix E(const ll n)
  {
    Matrix res(n, n);
    rep(i, n) rep(j, n) res[i][j] = (i == j);
    return res;
  }

  Matrix pow(const ll n)
  {
    assert(N == M);
    bitset<60> bs(n);
    int pow_cnt = 0;
    rep(i, 60) if (bs[i]) pow_cnt = i + 1;
    Matrix P = *this;
    Matrix res = E(N);

    rep(i, pow_cnt)
    {
      if (bs[i])
        res *= P;
      P *= P;
    }
    return res;
  }
};

template <typename T>
Matrix<T> operator*(ll a, Matrix<T> &A)
{
  Matrix<T> res(A.N, A.M);
  rep(i, A.N) rep(j, A.M) res[i][j] = A[i][j] * a;
  return res;
}

int main()
{
  init_main();

  ll m, k;
  cin >> m >> k;
  assert(1 <= m && m <= 50 && 1 <= k && k <= 1000000000);
  ll c[110][110] = {};
  rep(i, m) rep(j, m)
  {
    rep(t, m)
    {
      if ((i * t) % m == j)
        c[i][j]++;
    }
  }

  Matrix<mint> mt(m, m);
  rep(i, m) rep(j, m)
  {
    mt[i][j] = c[j][i] + 1;
  }
  mt = mt.pow(k);
  Matrix<mint> a(m, 1);
  rep(i, m) a[i][0] = (i == 0);
  a = mt * a;
  cout << a[0][0] << endl;

  return 0;
}