結果

問題 No.890 移調の限られた旋法
ユーザー FF256grhyFF256grhy
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
このコードへのチャレンジ
(要ログイン)
ファイルパターン 結果
sample AC * 3
other AC * 32
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 #
プレゼンテーションモードにする

#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;
}
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