結果

問題 No.890 移調の限られた旋法
ユーザー apricityapricity
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
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<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))
#endif
using 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_back
using 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);
}
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