結果

問題 No.2120 場合の数の下８桁
ユーザー leaf_1415leaf_1415
提出日時 2022-11-09 06:39:26
言語 C++11
(gcc 11.4.0)
結果
AC  
実行時間 801 ms / 2,000 ms
コード長 10,708 bytes
コンパイル時間 1,771 ms
コンパイル使用メモリ 113,640 KB
実行使用メモリ 159,872 KB
最終ジャッジ日時 2024-07-22 13:09:00
合計ジャッジ時間 18,447 ms
ジャッジサーバーID
（参考情報） 		judge1 / judge5
このコードへのチャレンジ
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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 728 ms
159,872 KB
testcase_01 AC 730 ms
159,724 KB
testcase_02 AC 728 ms
159,640 KB
testcase_03 AC 731 ms
159,872 KB
testcase_04 AC 731 ms
159,744 KB
testcase_05 AC 730 ms
159,720 KB
testcase_06 AC 727 ms
159,864 KB
testcase_07 AC 801 ms
159,872 KB
testcase_08 AC 794 ms
159,872 KB
testcase_09 AC 727 ms
159,872 KB
testcase_10 AC 728 ms
159,872 KB
testcase_11 AC 728 ms
159,860 KB
testcase_12 AC 729 ms
159,872 KB
testcase_13 AC 727 ms
159,744 KB
testcase_14 AC 727 ms
159,840 KB
testcase_15 AC 727 ms
159,744 KB
testcase_16 AC 728 ms
159,616 KB
testcase_17 AC 728 ms
159,872 KB
testcase_18 AC 727 ms
159,872 KB
testcase_19 AC 730 ms
159,744 KB
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ソースコード

diff # 

#include <iostream>
#include <iomanip>
#include <cstdio>
#include <cmath>
#include <ctime>
#include <cstdlib>
#include <cassert>
#include <vector>
#include <list>
#include <stack>
#include <queue>
#include <deque>
#include <map>
#include <set>
#include <bitset>
#include <string>
#include <algorithm>
#include <utility>
#include <complex>
#include <array>
#include <unordered_set>
#include <unordered_map>
#define rep(x, s, t) for(ll x = (s); (x) <= (t); (x)++)
#define per(x, s, t) for(ll x = (s); (x) >= (t); (x)--)
#define reps(x, s) for(ll x = 0; (x) < (ll)(s).size(); (x)++)
#define chmin(x, y) (x) = min((x), (y))
#define chmax(x, y) (x) = max((x), (y))
#define sz(x) ((ll)(x).size())
#define all(x) (x).begin(),(x).end()
#define rall(x) (x).rbegin(),(x).rend()
#define outl(...) dump_func(__VA_ARGS__)
#define outf(x) cout << fixed << setprecision(16) << (x) << endl
#define pb push_back
#define fi first
#define se second
#define inf 2e18
#define eps 1e-9
const double PI = 3.1415926535897932384626433;

using namespace std;

typedef long long ll;
typedef unsigned long long ull;
typedef pair<ll, ll> P;

struct edge{
	ll to, cost;
	edge(){}
	edge(ll a, ll b){ to = a, cost = b;}
};
const int dx[] = {1, 0, -1, 0}, dy[] = {0, -1, 0, 1};

const int mod = 1000000007;
//const int mod = 998244353;

struct mint{
	int x;
	mint(ll y = 0){if(y < 0 || y >= mod) y = (y%mod+mod)%mod; x = y;}
	mint(const mint &ope) {x = ope.x;}
	mint operator-(){return mint(-x);}
	mint operator+(const mint &ope){return mint(x) += ope;}
	mint operator-(const mint &ope){return mint(x) -= ope;}
	mint operator*(const mint &ope){return mint(x) *= ope;}
	mint operator/(const mint &ope){return mint(x) /= ope;}
	mint& operator+=(const mint &ope){x += ope.x; if(x >= mod) x -= mod; return *this;}
	mint& operator-=(const mint &ope){x += mod - ope.x; if(x >= mod) x -= mod; return *this;}
	mint& operator*=(const mint &ope){ll tmp = x; tmp *= ope.x, tmp %= mod; x = tmp; return *this;}
	mint& operator/=(const mint &ope){
		ll n = mod-2; mint mul = ope;
		while(n){if(n & 1) *this *= mul; mul *= mul; n >>= 1;}
		return *this;
	}
	mint inverse(){return mint(1) / *this;}
	bool operator ==(const mint &ope){return x == ope.x;}
	bool operator !=(const mint &ope){return x != ope.x;}
	bool operator <(const mint &ope)const{return x < ope.x;}
};
mint modpow(mint a, ll n){
	if(n == 0) return mint(1);
	if(n % 2) return a * modpow(a, n-1);
	else return modpow(a*a, n/2);
}
istream& operator >>(istream &is, mint &ope){ll t; is >> t, ope = mint(t); return is;}
ostream& operator <<(ostream &os, mint &ope){return os << ope.x;}
ostream& operator <<(ostream &os, const mint &ope){return os << ope.x;}

ll modpow(ll a, ll n, ll mod){
	if(n == 0) return 1;
	if(n % 2) return ((a%mod) * (modpow(a, n-1, mod)%mod)) % mod;
	else return modpow((a*a)%mod, n/2, mod) % mod;
}

vector<mint> fact, fact_inv;
void make_fact(int n){
	fact.resize(n+1), fact_inv.resize(n+1);
	fact[0] = mint(1); rep(i, 1, n) fact[i] = fact[i-1] * mint(i);
	fact_inv[n] = fact[n].inverse(); per(i, n-1, 0) fact_inv[i] = fact_inv[i+1] * mint(i+1);
}
mint comb(int n, int k){ if(n < 0 || k < 0 || n < k) return mint(0); return fact[n] * fact_inv[k] * fact_inv[n-k];}
mint perm(int n, int k){ return comb(n, k) * fact[k]; }
template<typename T> T comb2(ll n, ll k){ if(n < 0 || k < 0 || n < k) return T(0); T ret = 1; rep(i, 1, k) ret *= n-k+i, ret /= i; return ret;}

vector<int> prime, pvec, qrime;
void make_prime(int n){
	prime.resize(n+1);
	rep(i, 2, n){
		if(prime[i] == 0) pvec.push_back(i), prime[i] = i;
		for(auto p : pvec){ if(i*p > n || p > prime[i]) break; prime[i*p] = p;}
	}
}
void make_qrime(int n){
	qrime.resize(n+1);
	rep(i, 2, n){int ni = i / prime[i]; if(prime[i] == prime[ni]) qrime[i] = qrime[ni] * prime[i]; else qrime[i] = prime[i];}
}
void factorize(ll n, map<ll, ll> &mp){
	mp.clear();
	for(auto p : pvec) while(n % p == 0) mp[p]++, n /= p;
	if(n > 1) mp[n]++;
}

bool exceed(ll x, ll y, ll m){return y > 0 && x >= m / y + 1;}
void mark(){ cout << "*" << endl; }
void yes(){ cout << "YES" << endl; }
void no(){ cout << "NO" << endl; }
ll floor(ll a, ll b){ if(b < 0) a *= -1, b *= -1; if(a >= 0) return a/b; else return -((-a+b-1)/b); }
ll ceil(ll a, ll b){ if(b < 0) a *= -1, b *= -1; if(a >= 0) return (a+b-1)/b; else return -((-a)/b); }
ll modulo(ll a, ll b){ b = abs(b); return a - floor(a, b) * b;}
ll sgn(ll x){ if(x > 0) return 1; if(x < 0) return -1; return 0;}
ll gcd(ll a, ll b){if(b == 0) return a; return gcd(b, a%b);}
ll lcm(ll a, ll b){return a/gcd(a, b)*b;}
ll arith(ll x){return x*(x+1)/2;}
ll arith(ll l, ll r){return arith(r) - arith(l-1);}
ll digitnum(ll x, ll b = 10){ll ret = 0; for(; x; x /= b) ret++; return ret;}
ll digitsum(ll x, ll b = 10){ll ret = 0; for(; x; x /= b) ret += x % b; return ret;}
string lltos(ll x, ll b = 10){if(x == 0) return "0"; string ret; for(;x;x/=b) ret += x % b + '0'; reverse(all(ret)); return ret;}
ll stoll(string &s, ll b = 10){ll ret = 0; for(auto c : s) ret *= b, ret += c - '0'; return ret;}
template<typename T> void uniq(T &vec){sort(all(vec)); vec.erase(unique(all(vec)), vec.end());}
int popcount(ull x){
	x -= ((x>>1)&0x5555555555555555ULL), x = (x & 0x3333333333333333ULL) + ((x>>2) & 0x3333333333333333ULL);
	return (((x + (x>>4)) & 0x0F0F0F0F0F0F0F0FULL) * 0x0101010101010101ULL) >> 56;
}

template<class S, class T> pair<S, T>& operator+=(pair<S, T> &s, const pair<S, T> &t){s.first += t.first, s.second += t.second; return s;}
template<class S, class T> pair<S, T>& operator-=(pair<S, T> &s, const pair<S, T> &t){s.first -= t.first, s.second -= t.second; return s;}
template<class S, class T> pair<S, T> operator+(const pair<S, T> &s, const pair<S, T> &t){return pair<S,T>(s.first+t.first, s.second+t.second);}
template<class S, class T> pair<S, T> operator-(const pair<S, T> &s, const pair<S, T> &t){return pair<S,T>(s.first-t.first, s.second-t.second);}
template<class T> T dot(const pair<T, T> &s, const pair<T, T> &t){return s.first*t.first + s.second*t.second;}
template<class T> T cross(const pair<T, T> &s, const pair<T, T> &t){return s.first*t.second - s.second*t.first;}
template<class T> T mdist(pair<T, T> s, pair<T, T> t){return abs(s.first-t.first) + abs(s.second-t.second);}
template<class T> T cdist(pair<T, T> s, pair<T, T> t){return max(abs(s.first-t.first), abs(s.second-t.second));}
template<class T> T edist2(pair<T, T> s, pair<T, T> t){return (s.first-t.first)*(s.first-t.first) + (s.second-t.second)*(s.second-t.second);}

template<typename T> ostream& operator << (ostream& os, vector<T>& vec){reps(i, vec) os << vec[i] << " "; return os;}
template<typename T> ostream& operator << (ostream& os, const vector<T>& vec){reps(i, vec) os << vec[i] << " "; return os;}
template<typename T> ostream& operator << (ostream& os, list<T>& ls){for(auto x : ls) os << x << " "; return os;}
template<typename T> ostream& operator << (ostream& os, const list<T>& ls){for(auto x : ls) os << x << " "; return os;}
template<typename T> ostream& operator << (ostream& os, deque<T>& deq){reps(i,  deq) os << deq[i] << " "; return os;}
template<typename T, typename U> ostream& operator << (ostream& os, pair<T, U>& ope){ os << "(" << ope.first << ", " << ope.second << ")"; return os;}
template<typename T, typename U> ostream& operator << (ostream& os, const pair<T, U>& ope){ os << "(" << ope.first << ", " << ope.second << ")"; return os;}
template<typename T, typename U> ostream& operator << (ostream& os, map<T, U>& ope){ for(auto p : ope) os << "(" << p.first << ", " << p.second << "),";return os;}
template<typename T> ostream& operator << (ostream& os, set<T>& ope){for(auto x : ope) os << x << " "; return os;}
template<typename T> ostream& operator << (ostream& os, multiset<T>& ope){for(auto x : ope) os << x << " "; return os;}
template<typename T> void outa(T a[], ll s, ll t){rep(i, s, t){ cout << a[i]; if(i < t) cout << " ";} cout << endl;}
template<typename T, size_t N> ostream& operator << (ostream& os, array<T, N>& arr){reps(i, arr) os << arr[i] << " "; return os;}
template<typename T, size_t N> ostream& operator << (ostream& os, const array<T, N>& arr){reps(i, arr) os << arr[i] << " "; return os;}
void dump_func(){cout << endl;}
template <class Head, class... Tail>
void dump_func(Head &&head, Tail &&... tail){cout << head; if(sizeof...(Tail) > 0) cout << " "; dump_func(std::move(tail)...);}


struct Congruence{
	//ax+by = gcd(a, b)を満たす(x, y)を求めgcd(a, b)を返す
	static ll extgcd(ll a, ll b, ll &x, ll &y)
	{
		if(b == 0){
			x = 1, y = 0;
			return a;
		}
		ll xx, yy;
		ll d = extgcd(b, a%b, xx, yy);
		x = yy, y = xx-(a/b)*yy;
		return d;
	}

	//a^{-1} (mod m)を求める。存在しない場合(gcd(a, m)!=1)は-1を返す
	static ll mod_inverse(ll a, ll m)
	{
		ll x, y;
		if(extgcd(a, m, x, y) != 1) return -1;
		return (x%m + m) % m;
	}

	//ax = b (mod m)を満たすx(mod m/gcd(a, m))を求める。存在しない場合(b%gcd(a, m)!=0)は(0, -1)を返す
	static P congruence(ll a, ll b, ll m)
	{
		ll d = gcd(a, m);
		if(b % d) return make_pair(0, -1);
		a /= d, b /= d, m /= d;
		return make_pair(b * mod_inverse(a, m) % m, m);
	}

	//連立合同方程式a_i*x = b_i (mod m_i)(i = 1, 2, ..., n)の解(x, M)を求める。存在しない場合(0, -1)を返す
	static P simultaneous(ll a[], ll b[], ll m[], ll n)
	{
		ll x = 0, M = 1;
		for(int i = 1; i <= n; i++){
			P res = congruence(a[i]*M, (b[i]-a[i]*x%m[i]+m[i])%m[i], m[i]);
			if(res.second == -1) return res;
			x += M*res.first, M *= res.second;
		}
		return make_pair(x, M);
	}
};

const int FACT_MAX = 10000005;
ll q[FACT_MAX], e[FACT_MAX];

void make_fact(ll p, ll mod)
{
	ll qval = 1, eval = 0;
	q[0] = 1, e[0] = 0;
	
	for(int i = 1; i < FACT_MAX; i++){
		ll t = i;
		while(t % p == 0) eval++, t /= p;
		qval *= t, qval %= mod;
		q[i] = qval, e[i] = eval;
	}
}

ll comb(ll n, ll k, ll p, ll ex, ll mod)
{
	if(n < 0 || k < 0 || n < k) return 0;
	ll eval = e[n] - e[k] - e[n-k];
	if(eval >= ex) return 0;
	
	ll ret = q[n] * Congruence::mod_inverse(q[k]*q[n-k]%mod, mod) % mod;
	ret *= modpow(p, eval, mod), ret %= mod;
	return ret;
}

ll n, k;
ll calc(ll p, ll ex, ll mod)
{
	make_fact(p, mod);
	
	//mod = p^exのときの答えを求める処理を書く
	
	return comb(n, k, p, ex, mod);
}

const ll M = 100000000;

//Mを法とする
int main(void)
{
	cin >> n >> k;
	
	map<ll, ll> mp;
	make_prime(sqrt(M+5));
	factorize(M, mp);
	
	ll id = 0, a[55], b[55], m[55];
	for(auto it = mp.begin(); it != mp.end(); it++){
		id++;
		ll mod = 1;
		for(int i = 0; i < it->second; i++) mod *= it->first;
		a[id] = 1, b[id] = calc(it->first, it->second, mod), m[id] = mod;
	}
	printf("%08d\n", (int)Congruence::simultaneous(a, b, m, id).first);
	
	return 0;
}
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