結果
問題 | No.890 移調の限られた旋法 |
ユーザー |
![]() |
提出日時 | 2023-03-21 15:57:13 |
言語 | C++17 (gcc 13.3.0 + boost 1.87.0) |
結果 |
AC
|
実行時間 | 158 ms / 2,000 ms |
コード長 | 8,214 bytes |
コンパイル時間 | 1,267 ms |
コンパイル使用メモリ | 135,428 KB |
最終ジャッジ日時 | 2025-02-11 15:52:33 |
ジャッジサーバーID (参考情報) |
judge4 / judge2 |
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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<iostream>#include<string>#include<vector>#include<algorithm>#include<numeric>#include<cmath>#include<utility>#include<tuple>#include<cstdint>#include<cstdio>#include<iomanip>#include<map>#include<queue>#include<set>#include<stack>#include<deque>#include<unordered_map>#include<unordered_set>#include<bitset>#include<cctype>#include<chrono>#include<random>#include<cassert>#include<cstddef>#include<iterator>#include<string_view>#include<type_traits>#ifdef LOCAL# include "debug_print.hpp"# define debug(...) debug_print::multi_print(#__VA_ARGS__, __VA_ARGS__)#else# define debug(...) (static_cast<void>(0))#endifusing namespace std;#define rep(i,n) for(int i=0; i<(n); i++)#define rrep(i,n) for(int i=(n)-1; i>=0; i--)#define FOR(i,a,b) for(int i=(a); i<(b); i++)#define RFOR(i,a,b) for(int i=(b-1); i>=(a); i--)#define ALL(v) v.begin(), v.end()#define RALL(v) v.rbegin(), v.rend()#define UNIQUE(v) v.erase( unique(v.begin(), v.end()), v.end() );#define pb push_backusing ll = long long;using D = double;using LD = long double;using P = pair<int, int>;template<typename T> using PQ = priority_queue<T,vector<T>>;template<typename T> using minPQ = priority_queue<T, vector<T>, greater<T>>;template<class T>bool chmax(T &a, const T &b) { if (a<b) { a=b; return 1; } return 0; }template<class T>bool chmin(T &a, const T &b) { if (b<a) { a=b; return 1; } return 0; }void yesno(bool flag) {cout << (flag?"Yes":"No") << "\n";}template<typename T, typename U>ostream &operator<<(ostream &os, const pair<T, U> &p) {os << p.first << " " << p.second;return os;}template<typename T, typename U>istream &operator>>(istream &is, pair<T, U> &p) {is >> p.first >> p.second;return is;}template<typename T>ostream &operator<<(ostream &os, const vector<T> &v) {int s = (int)v.size();for (int i = 0; i < s; i++) os << (i ? " " : "") << v[i];return os;}template<typename T>istream &operator>>(istream &is, vector<T> &v) {for (auto &x : v) is >> x;return is;}void in() {}template<typename T, class... U>void in(T &t, U &...u) {cin >> t;in(u...);}void out() { cout << "\n"; }template<typename T, class... U, char sep = ' '>void out(const T &t, const U &...u) {cout << t;if (sizeof...(u)) cout << sep;out(u...);}void outr() {}template<typename T, class... U, char sep = ' '>void outr(const T &t, const U &...u) {cout << t;outr(u...);}template<int mod> struct Fp {long long val;constexpr Fp(long long v = 0) noexcept : val(v % mod) {if (val < 0) val += mod;}constexpr int getmod() { return mod; }constexpr Fp operator - () const noexcept {return val ? mod - val : 0;}constexpr Fp operator + (const Fp& r) const noexcept { return Fp(*this) += r; }constexpr Fp operator - (const Fp& r) const noexcept { return Fp(*this) -= r; }constexpr Fp operator * (const Fp& r) const noexcept { return Fp(*this) *= r; }constexpr Fp operator / (const Fp& r) const noexcept { return Fp(*this) /= r; }constexpr Fp& operator += (const Fp& r) noexcept {val += r.val;if (val >= mod) val -= mod;return *this;}constexpr Fp& operator -= (const Fp& r) noexcept {val -= r.val;if (val < 0) val += mod;return *this;}constexpr Fp& operator *= (const Fp& r) noexcept {val = val * r.val % mod;return *this;}constexpr Fp& operator /= (const Fp& r) noexcept {long long a = r.val, b = mod, u = 1, v = 0;while (b) {long long t = a / b;a -= t * b; swap(a, b);u -= t * v; swap(u, v);}val = val * u % mod;if (val < 0) val += mod;return *this;}constexpr bool operator == (const Fp& r) const noexcept {return this->val == r.val;}constexpr bool operator != (const Fp& r) const noexcept {return this->val != r.val;}friend constexpr ostream& operator << (ostream &os, const Fp<mod>& x) noexcept {return os << x.val;}friend constexpr Fp<mod> modpow(const Fp<mod> &a, long long n) noexcept {if (n == 0) return 1;auto t = modpow(a, n / 2);t = t * t;if (n & 1) t = t * a;return t;}};template<class T> struct BiCoef {vector<T> fact_, inv_, finv_;constexpr BiCoef() {}constexpr BiCoef(int n) noexcept : fact_(n, 1), inv_(n, 1), finv_(n, 1) {init(n);}constexpr void init(int n) noexcept {fact_.assign(n, 1), inv_.assign(n, 1), finv_.assign(n, 1);int mod = fact_[0].getmod();for(int i = 2; i < n; i++){fact_[i] = fact_[i-1] * i;inv_[i] = -inv_[mod%i] * (mod/i);finv_[i] = finv_[i-1] * inv_[i];}}constexpr T com(int n, int k) const noexcept {if (n < k || n < 0 || k < 0) return 0;return fact_[n] * finv_[k] * finv_[n-k];}constexpr T perm(int n, int k) const noexcept {if (n < k || n < 0 || k < 0) return 0;return fact_[n] * finv_[n-k];}constexpr T fact(int n) const noexcept {if (n < 0) return 0;return fact_[n];}constexpr T inv(int n) const noexcept {if (n < 0) return 0;return inv_[n];}constexpr T finv(int n) const noexcept {if (n < 0) return 0;return finv_[n];}};const int mod = 1e9+7;// const int mod = 998244353;using mint = Fp<mod>;BiCoef<mint> bc;struct eratosthenes{vector<bool> isprime;vector<int> minfactor;vector<int> mobius;eratosthenes(int n) : isprime(n+1,true), minfactor(n+1, -1), mobius(n+1,1){isprime[1] = false;minfactor[1] = 1;for(int i = 2; i <= n; i++){if(!isprime[i]) continue;minfactor[i] = i;mobius[i] = -1;for(int j = i+i; j <= n; j += i){isprime[j] = false;if(minfactor[j] == -1) minfactor[j] = i;if((j/i)%i == 0) mobius[j] = 0;else mobius[j] *= -1;}}}vector<pair<int, int>> factorize(int n){vector<pair<int, int>> res;while(n > 1){int p = minfactor[n];int e = 0;while(minfactor[n] == p){n /= p;e++;}res.push_back({p,e});}return res;}vector<int> divisor(int n){vector<int> res;res.pb(1);auto v = factorize(n);for(auto x : v){int s = res.size();rep(i,s){int m = 1;rep(j,x.second){m *= x.first;res.push_back(res[i]*m);}}}return res;}template<class T> void fzt(vector<T> &f){int n = f.size();for(int p = 2; p < n; p++){if(!isprime[p]) continue;for(int q = (n-1)/p; q > 0; q--){f[q] += f[p*q];}}}template<class T> void fmt(vector<T> &f){int n = f.size();for(int p = 2; p < n; p++){if(!isprime[p]) continue;for(int q = 1; q*p < n; q++){f[q] -= f[p*q];}}}template<class T> vector<T> conv(const vector<T> &f, const vector<T> &g){int n = max(f.size(), g.size());vector<T> nf(n), ng(n), h(n);rep(i,f.size()) nf[i] = f[i];rep(i,g.size()) ng[i] = g[i];fzt(nf); fzt(ng);rep(i,n) h[i] = nf[i]*ng[i];fmt(h);return h;}};int main(){ios_base::sync_with_stdio(false);cin.tie(nullptr);int n,k; in(n,k);bc.init(n+1);eratosthenes si(n+1);vector<mint> cnt(n+1);FOR(i,1,n+1){int g = gcd(n,i);if(k%(n/g) == 0){cnt[i] = bc.com(g, k/(n/g));}}mint fn = 0;for(int e : si.divisor(n)){fn += cnt[e] * si.mobius[n/e];}out(bc.com(n,k) - fn);}