結果
問題 | No.890 移調の限られた旋法 |
ユーザー |
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提出日時 | 2019-09-20 22:31:11 |
言語 | C++14 (gcc 13.3.0 + boost 1.87.0) |
結果 |
AC
|
実行時間 | 23 ms / 2,000 ms |
コード長 | 4,711 bytes |
コンパイル時間 | 1,686 ms |
コンパイル使用メモリ | 174,052 KB |
実行使用メモリ | 11,320 KB |
最終ジャッジ日時 | 2024-09-14 18:25:23 |
合計ジャッジ時間 | 3,144 ms |
ジャッジサーバーID (参考情報) |
judge1 / judge3 |
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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>using namespace std;typedef long long signed int LL;typedef long long unsigned int LU;#define incID(i, l, r) for(LL i = (l) ; i < (r); ++i)#define incII(i, l, r) for(LL i = (l) ; i <= (r); ++i)#define decID(i, l, r) for(LL i = (r) - 1; i >= (l); --i)#define decII(i, l, r) for(LL i = (r) ; i >= (l); --i)#define inc(i, n) incID(i, 0, n)#define inc1(i, n) incII(i, 1, n)#define dec(i, n) decID(i, 0, n)#define dec1(i, n) decII(i, 1, n)#define inID(v, l, r) ((l) <= (v) && (v) < (r))#define inII(v, l, r) ((l) <= (v) && (v) <= (r))#define PB push_back#define EB emplace_back#define MP make_pair#define FI first#define SE second#define ALL(v) v.begin(), v.end()#define RALL(v) v.rbegin(), v.rend()template<typename T> bool setmin (T & a, T b) { if(b < a) { a = b; return true; } else { return false; } }template<typename T> bool setmax (T & a, T b) { if(b > a) { a = b; return true; } else { return false; } }template<typename T> bool setmineq(T & a, T b) { if(b <= a) { a = b; return true; } else { return false; } }template<typename T> bool setmaxeq(T & a, T b) { if(b >= a) { a = b; return true; } else { return false; } }LL mo(LL a, LL b) { assert(b > 0); a %= b; if(a < 0) { a += b; } return a; }LL fl(LL a, LL b) { assert(b > 0); return (a > 0 ? a / b : (a - b + 1) / b); }LL ce(LL a, LL b) { assert(b > 0); return (a < 0 ? a / b : (a + b - 1) / b); }template<typename T> T gcd(T a, T b) { return (b == 0 ? a : gcd(b, a % b)); }template<typename T> T lcm(T a, T b) { return a / gcd(a, b) * b; }#define bit(b, i) (((b) >> (i)) & 1)#define BC __builtin_popcountll#define SC static_cast#define SI(v) SC<int>(v.size())#define SL(v) SC<LL >(v.size())#define RF(e, v) for(auto & e: v)#define ef else if#define UR assert(false)// ---- ----template<LL M> class ModInt {private:LL v = 0;public:ModInt() { }ModInt(LL vv) { setval(vv); }ModInt & setval(LL vv) { v = vv % M; if(v < 0) { v += M; } return (*this); }LL getval() const { return v; }ModInt & operator+=(const ModInt & b) { return setval(v + b.v); }ModInt & operator-=(const ModInt & b) { return setval(v - b.v); }ModInt & operator*=(const ModInt & b) { return setval(v * b.v); }ModInt & operator/=(const ModInt & b) { return setval(v * b.inv()); }ModInt & operator^=( LU b) { return setval(ex(v, b)); }ModInt operator+ ( ) const { return ModInt(+v); }ModInt operator- ( ) const { return ModInt(-v); }ModInt operator+ (const ModInt & b) const { return ModInt(v + b.v); }ModInt operator- (const ModInt & b) const { return ModInt(v - b.v); }ModInt operator* (const ModInt & b) const { return ModInt(v * b.v); }ModInt operator/ (const ModInt & b) const { return ModInt(v * b.inv()); }ModInt operator^ ( LU b) const { return ModInt(ex(v, b)); }LL inv() const {LL x = (ex_gcd(v, M).FI + M) % M;assert(v * x % M == 1);return x;}LL ex(LL a, LU b) const {LL D = 64, x[64], y = 1;inc(i, D) { if((b >> i) == 0) { D = i; break; } }inc(i, D) { x[i] = (i == 0 ? a : x[i - 1] * x[i - 1]) % M; }inc(i, D) { if((b >> i) & 1) { (y *= x[i]) %= M; } }return y;}pair<LL, LL> ex_gcd(LL a, LL b) const {if(b == 0) { return MP(1, 0); }auto p = ex_gcd(b, a % b);return MP(p.SE, p.FI - (a / b) * p.SE);}};template<LL M> ModInt<M> operator+(LL a, const ModInt<M> & b) { return b + a; }template<LL M> ModInt<M> operator-(LL a, const ModInt<M> & b) { return -b + a; }template<LL M> ModInt<M> operator*(LL a, const ModInt<M> & b) { return b * a; }template<LL M> ModInt<M> operator/(LL a, const ModInt<M> & b) { return a * b.inv(); }template<LL M> istream & operator>>(istream & is, ModInt<M> & b) { LL v; is >> v; b.setval(v); return is; }template<LL M> ostream & operator<<(ostream & os, const ModInt<M> & b) { return (os << b.getval()); }// ---- ----typedef ModInt<1'000'000'007> MI;MI f[1000001];MI comb(LL x, LL y) {return f[x] / (f[y] * f[x - y]);}vector<pair<LL, LL>> prime_factorization(LL x) {assert(x > 0);vector<pair<LL, LL>> f;for(LL i = 2; i <= x; i++) {if(i * i > x) { i = x; }if(x % i == 0) {f.EB(i, 0);while(x % i == 0) { f.back().SE++; x /= i; }}}return f;}LL mu(LL x) {auto f = prime_factorization(x);RF(e, f) {if(e.SE > 1) { return 0; }}return (SI(f) % 2 == 0 ? 1 : -1);}LL n, k;int main() {cin >> n >> k;incII(i, 0, n) { f[i] = (i == 0 ? 1 : f[i - 1] * i); }MI ans = comb(n, k);inc1(d, n) {if(n % d == 0 && k % d == 0) {ans -= mu(d) * (k % d == 0 ? comb(n / d, k / d) : 0);}}cout << ans << endl;return 0;}