結果
問題 | No.890 移調の限られた旋法 |
ユーザー | apricity |
提出日時 | 2023-03-21 15:57:13 |
言語 | C++17 (gcc 12.3.0 + boost 1.83.0) |
結果 |
AC
|
実行時間 | 171 ms / 2,000 ms |
コード長 | 8,214 bytes |
コンパイル時間 | 1,680 ms |
コンパイル使用メモリ | 141,060 KB |
実行使用メモリ | 42,544 KB |
最終ジャッジ日時 | 2024-09-18 14:23:19 |
合計ジャッジ時間 | 5,386 ms |
ジャッジサーバーID (参考情報) |
judge5 / judge2 |
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テストケース
テストケース表示入力 | 結果 | 実行時間 実行使用メモリ |
---|---|---|
testcase_00 | AC | 2 ms
5,248 KB |
testcase_01 | AC | 2 ms
5,376 KB |
testcase_02 | AC | 2 ms
5,376 KB |
testcase_03 | AC | 2 ms
5,376 KB |
testcase_04 | AC | 2 ms
5,376 KB |
testcase_05 | AC | 2 ms
5,376 KB |
testcase_06 | AC | 2 ms
5,376 KB |
testcase_07 | AC | 2 ms
5,376 KB |
testcase_08 | AC | 2 ms
5,376 KB |
testcase_09 | AC | 2 ms
5,376 KB |
testcase_10 | AC | 2 ms
5,376 KB |
testcase_11 | AC | 2 ms
5,376 KB |
testcase_12 | AC | 2 ms
5,376 KB |
testcase_13 | AC | 158 ms
42,368 KB |
testcase_14 | AC | 157 ms
42,544 KB |
testcase_15 | AC | 160 ms
42,368 KB |
testcase_16 | AC | 171 ms
42,496 KB |
testcase_17 | AC | 144 ms
38,400 KB |
testcase_18 | AC | 148 ms
38,468 KB |
testcase_19 | AC | 52 ms
23,804 KB |
testcase_20 | AC | 54 ms
16,336 KB |
testcase_21 | AC | 12 ms
6,144 KB |
testcase_22 | AC | 120 ms
33,280 KB |
testcase_23 | AC | 156 ms
39,936 KB |
testcase_24 | AC | 84 ms
24,264 KB |
testcase_25 | AC | 20 ms
8,192 KB |
testcase_26 | AC | 152 ms
40,704 KB |
testcase_27 | AC | 165 ms
41,452 KB |
testcase_28 | AC | 100 ms
27,704 KB |
testcase_29 | AC | 67 ms
19,200 KB |
testcase_30 | AC | 139 ms
38,400 KB |
testcase_31 | AC | 83 ms
23,296 KB |
testcase_32 | AC | 133 ms
35,712 KB |
testcase_33 | AC | 145 ms
37,760 KB |
testcase_34 | AC | 153 ms
37,760 KB |
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)) #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); }