結果

問題 No.890 移調の限られた旋法
ユーザー Haar
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
このコードへのチャレンジ
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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>
#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init
*/
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
*
* mu(n) = (-1)^k if nk
*
* mu(nm) = mu(n) * mu(m) if nm
*/
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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