Submission #675935

#	Time	Username	Problem	Language	Result	Execution time	Memory
675935		QwertyPi	Energetic turtle (IZhO11_turtle)	C++14	100 / 100	257 ms	141260 KiB

turtle

#include <bits/stdc++.h>
#define fi first
#define se second
#define int long long
using namespace std;

const int MAXN = 6e5 + 11;

int phi = 1;
map<int, int> pf;

map<int, int> f[MAXN] = {}; 

int pm(int a, int b, int Z){
	a %= Z;
	if(b == 0) return 1;
	return pm(a * a % Z, b / 2, Z) * (b % 2 ? a : 1) % Z;
}

int mi(int a, int Z){
	a %= Z;
	return pm(a, phi - 1, Z);
} 

int C(int n, int r, int Z){
	if(n < r || r < 0 || n < 0) return 0;
	map<int, int> res; res[0] = 1;
	for(auto i : f[n]){
		if(i.fi == 0){
			res[0] = (res[0] * i.se) % Z;
		}else{
			res[i.fi] += i.se;
		}
	}
	for(auto i : f[r]){
		if(i.fi == 0){
			res[0] = (res[0] * mi(i.se, Z)) % Z;
		}else{
			res[i.fi] -= i.se;
		}
	}
	for(auto i : f[n - r]){
		if(i.fi == 0){
			res[0] = (res[0] * mi(i.se, Z)) % Z;
		}else{
			res[i.fi] -= i.se;
		}
	}
	int ans = 1;
	for(auto i : res){
		if(i.fi == 0){
			ans *= i.se; ans %= Z;
			continue;
		}
		for(int j = 0; j < i.se; j++){
			ans *= i.fi; ans %= Z;
		}
	}
	return ans;
}

int p[25][2], d[25][25];
int Cu[25];

int32_t main(){
	int64_t N, M, K, T, Z;
	cin >> N >> M >> K >> T >> Z;
	phi = Z;
	int z = Z;
	for(int i = 2; i <= sqrt(1e9) + 11; i++){
		if(z % i == 0) phi = phi / i * (i - 1);
		while(z % i == 0) pf[i]++, z /= i;
	}
	if(z != 1) phi = phi / z * (z - 1), pf[z]++;
	
	f[0][0] = 1;
	for(int i = 1; i <= MAXN - 1; i++){
		f[i] = f[i - 1];
		int x = i;
		for(auto p : pf){
			while(x % p.fi == 0){
				f[i][p.fi]++; x /= p.fi;
			}
		}
		f[i][0] = f[i - 1][0] * x % Z;
	}
	p[0][0] = 0, p[0][1] = 0;
	p[K + 1][0] = N, p[K + 1][1] = M;
	
	vector<pair<int, int>> v;
	for(int i = 0; i < K; i++){
		int64_t x, y; cin >> x >> y;
		v.push_back({x, y});
	}
	sort(v.begin(), v.end());
	for(int i = 1; i <= K; i++){
		p[i][0] = v[i - 1].fi, p[i][1] = v[i - 1].se;
	}
	
	for(int i = 0; i <= K + 1; i++){
		for(int j = i + 1; j <= K + 1; j++){
			int dx = p[j][0] - p[i][0];
			int dy = p[j][1] - p[i][1];
			if(dx >= 0 && dy >= 0) d[i][j] = C(dx + dy, dx, Z);
		}
	}
	
	for(int i = 0; i <= K; i++){
		Cu[i] = C(i - 1, T, Z);
	}
	
	int s = C(N + M, N, Z), t = 0;
	for(int i = 0; i < (1 << K); i++){
		int U = __builtin_popcount(i);
		int f = 1, pv = 0;
		for(int j = 0; j < K; j++){
			if(i & (1 << j)){
				f = f * d[pv][j + 1] % Z;
				pv = j + 1;
			}
		}
		f = f * d[pv][K + 1] % Z;
		t += ((U + T + 1) % 2 ? -1 : 1) * Cu[U] * f % Z;
		t %= Z;
	}
	cout << (long long)((s - t) % Z + Z) % Z << endl;
}

• Subtask 1: 100 / 100