結果
問題 |
No.890 移調の限られた旋法
|
ユーザー |
|
提出日時 | 2019-09-20 22:13:54 |
言語 | C++17 (gcc 13.3.0 + boost 1.87.0) |
結果 |
AC
|
実行時間 | 123 ms / 2,000 ms |
コード長 | 6,817 bytes |
コンパイル時間 | 2,459 ms |
コンパイル使用メモリ | 203,264 KB |
最終ジャッジ日時 | 2025-01-07 18:44:49 |
ジャッジサーバーID (参考情報) |
judge1 / judge1 |
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ファイルパターン | 結果 |
---|---|
sample | AC * 3 |
other | AC * 32 |
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 <misc/C++/Debug.cpp>#else#define dump(...) ((void)0)#endif#define gcd __gcdusing 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;}