結果

問題 No.890 移調の限られた旋法
ユーザー HaarHaar
提出日時 2019-09-20 22:13:54
言語 C++17
(gcc 12.3.0 + boost 1.83.0)
結果
AC  
実行時間 111 ms / 2,000 ms
コード長 6,817 bytes
コンパイル時間 2,537 ms
コンパイル使用メモリ 211,804 KB
実行使用メモリ 30,896 KB
最終ジャッジ日時 2024-09-14 17:58:44
合計ジャッジ時間 6,402 ms
ジャッジサーバーID
（参考情報） 		judge5 / judge1
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テストケース

テストケース表示
入力 結果 実行時間
実行使用メモリ
testcase_00 AC 65 ms
23,424 KB
testcase_01 AC 59 ms
23,380 KB
testcase_02 AC 65 ms
23,424 KB
testcase_03 AC 60 ms
23,416 KB
testcase_04 AC 59 ms
23,392 KB
testcase_05 AC 59 ms
23,340 KB
testcase_06 AC 60 ms
23,424 KB
testcase_07 AC 59 ms
23,296 KB
testcase_08 AC 59 ms
23,388 KB
testcase_09 AC 59 ms
23,424 KB
testcase_10 AC 59 ms
23,388 KB
testcase_11 AC 60 ms
23,424 KB
testcase_12 AC 58 ms
23,356 KB
testcase_13 AC 100 ms
30,768 KB
testcase_14 AC 100 ms
30,824 KB
testcase_15 AC 99 ms
30,700 KB
testcase_16 AC 98 ms
30,896 KB
testcase_17 AC 105 ms
30,000 KB
testcase_18 AC 105 ms
29,992 KB
testcase_19 AC 78 ms
27,160 KB
testcase_20 AC 70 ms
25,588 KB
testcase_21 AC 61 ms
23,468 KB
testcase_22 AC 84 ms
28,844 KB
testcase_23 AC 86 ms
30,372 KB
testcase_24 AC 80 ms
27,180 KB
testcase_25 AC 64 ms
23,980 KB
testcase_26 AC 97 ms
30,512 KB
testcase_27 AC 84 ms
30,508 KB
testcase_28 AC 78 ms
27,772 KB
testcase_29 AC 73 ms
26,156 KB
testcase_30 AC 111 ms
30,028 KB
testcase_31 AC 85 ms
27,044 KB
testcase_32 AC 109 ms
29,572 KB
testcase_33 AC 101 ms
29,740 KB
testcase_34 AC 102 ms
29,812 KB
権限があれば一括ダウンロードができます

ソースコード

diff # 

#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 <misc/C++/Debug.cpp>
#else
#define dump(...) ((void)0)
#endif

#define gcd __gcd

using namespace std;
template <class T> constexpr T lcm(T m, T n){return m/gcd(m,n)*n;}

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, 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);}

struct Init{
  Init(){
    cin.tie(0);
    ios::sync_with_stdio(false);
  }
}init;

template <uint32_t M> class ModInt{
public:
  uint64_t val;
  ModInt(): val(0){}
  ModInt(int64_t n){
    if(n >= M) val = n % M;
    else if(n < 0) val = n % M + M;
    else val = n;
  }
  
  inline constexpr ModInt operator+(const ModInt &a) const {return ModInt((val+a.val)%M);}
  inline constexpr ModInt operator-(const ModInt &a) const {return ModInt((val-a.val+M)%M);}
  inline constexpr ModInt operator*(const ModInt &a) const {return ModInt((val*a.val)%M);}
  inline constexpr ModInt operator/(const ModInt &a) const {return ModInt((val*a.inv().val)%M);}
  
  inline constexpr ModInt& operator=(const ModInt &a){val = a.val; return *this;}
  inline constexpr ModInt& operator+=(const ModInt &a){if((val += a.val) >= M) val -= M; return *this;}
  inline constexpr ModInt& operator-=(const ModInt &a){if(val < a.val) val += M; val -= a.val; return *this;}
  inline constexpr ModInt& operator*=(const ModInt &a){(val *= a.val) %= M; return *this;}
  inline constexpr ModInt& 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 ModInt& operator++(){*this += 1; return *this;}
  inline constexpr ModInt& operator--(){*this -= 1; return *this;}

  inline constexpr ModInt operator++(int){ModInt t = *this; *this += 1; return t;}
  inline constexpr ModInt operator--(int){ModInt t = *this; *this -= 1; return t;}
  
  inline constexpr static ModInt power(LLI n, LLI p){
    ModInt ret = 1, e = n;
    for(; p; e *= e, p >>= 1) if(p&1) ret *= e;
    return ret;
  }

  inline constexpr ModInt power(LLI p) const {return power(val,p);}
  
  inline constexpr ModInt inv() const {
    int64_t a = val, b = M, u = 1, v = 0;

    while(b){
      int64_t t = a/b;
      a -= t*b; swap(a,b);
      u -= t*v; swap(u,v);
    }
    u %= M;
    if(u < 0) u += M;
    
    return u;
  }
};

template <uint32_t M> ModInt<M> operator-(const ModInt<M> &a){return M-a.val;}

template <uint32_t M> ModInt<M> operator+(int64_t a, const ModInt<M> &b){return ModInt<M>(ModInt<M>(a)+b.val);}
template <uint32_t M> ModInt<M> operator-(int64_t a, const ModInt<M> &b){return ModInt<M>(ModInt<M>(a)-b.val);}
template <uint32_t M> ModInt<M> operator*(int64_t a, const ModInt<M> &b){return ModInt<M>(ModInt<M>(a)*b.val);}
template <uint32_t M> ModInt<M> operator/(int64_t a, const ModInt<M> &b){return ModInt<M>(ModInt<M>(a)/b.val);}

template <uint32_t M> istream& operator>>(istream &is, ModInt<M> &a){is >> a.val; return is;}
template <uint32_t M> ostream& operator<<(ostream &os, const ModInt<M> &a){ os << a.val; return os;}

using mint = ModInt<1000000007>;

/**
 * @attention 使用前にinit関数を呼び出す
 */
template <typename T> class CombUtilsMint{
public:
  static vector<T> facto;
  static vector<T> ifacto;

  static void init(int N){
    facto.assign(N+1, 1);
    ifacto.assign(N+1, 1);

    FORE(i,1,N){
      facto[i] = facto[i-1] * i;
    }

    ifacto[N] = facto[N].inv();

    REV(i,N-1,0){
      ifacto[i] = ifacto[i+1] * (i+1);
    }
  }

  static T f(LLI i){
    assert(i < facto.size());
    return facto[i];
  }
  
  static T finv(LLI i){
    assert(i < ifacto.size());
    return ifacto[i];
  }

  static T P(LLI n, LLI k);
  static T C(LLI n, LLI k);
  static T H(LLI n, LLI k);
  static T stirling_number(LLI n, LLI k);
  static T bell_number(LLI n, LLI k);
  static vector<T> bernoulli_number(LLI n);
};

template <typename T> vector<T> CombUtilsMint<T>::facto = vector<T>();
template <typename T> vector<T> CombUtilsMint<T>::ifacto = vector<T>();

template <typename T> T CombUtilsMint<T>::P(LLI n, LLI k){
  if(n < k or n < 0 or k < 0) return 0;
  return f(n) * finv(n-k);
}

template <typename T> T CombUtilsMint<T>::C(LLI n, LLI k){
  if(n < k or n < 0 or k < 0) return 0;
  return P(n,k) * finv(k);
}

template <typename T> T CombUtilsMint<T>::H(LLI n, LLI k){
  if(n == 0 and k == 0) return 1;
  return C(n+k-1, k);
}


vector<bool> eratosthenes_sieve(int n){
  vector<bool> res(n+1, true);
  res[0] = res[1] = false;
  FOR(i,2,n) if(res[i]) for(int j=2*i; j<=n; j+=i) res[j] = false;
  return res;
}

auto is_prime = eratosthenes_sieve(1000000);



/**
 * @details
 * mu(1) = 1
 *
 * mu(n) = 0 if nが平方因子を持つ
 *
 * mu(n) = (-1)^k if nが相異なるk個の素因数に分解される
 *
 * mu(nm) = mu(n) * mu(m) if nとmが互いに素
 */
vector<int> mobius(int n){
  vector<int> ret(n+1);
  vector<int> ps;
  ret[1] = 1;
  FORE(i,2,n){
    if(is_prime[i]){
      ps.push_back(i);
      ret[i] = -1;
    }
    for(auto &j : ps){
      if(i*j > n) break;
      if(i%j == 0) ret[i*j] = 0;
      else ret[i*j] = ret[i] * ret[j];
    }
  }
  
  return ret;
}

using C = CombUtilsMint<mint>;


int main(){
  C::init(1000000);
  auto m = mobius(1000000);
  
  int N,K;
  while(cin >> N >> K){
    vector<mint> f(N+1);

    FOR(i,1,N){
      if(N % i == 0){
        int d = N/i;

        if(K % d == 0){
          f[i] = C::C(i,K/d);
        }
      }
    }

    mint ans = 0;

    FOR(i,1,N){
      if(N % i != 0) continue;
      
      FORE(j,1,i){
        if(i % j == 0){
          ans += m[i/j] * f[j];
        }
      }
    }

    cout << ans << endl;
  }

  return 0;
}
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