Submission #1256442

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Source Code Expand

#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef vector<int> vint;
typedef pair<int,int> pint;
typedef vector<pint> vpint;
#define rep(i,n) for(int i=0;i<(n);i++)
#define REP(i,n) for(int i=n-1;i>=(0);i--)
#define reps(i,f,n) for(int i=(f);i<(n);i++)
#define each(it,v) for(__typeof((v).begin()) it=(v).begin();it!=(v).end();it++)
#define all(v) (v).begin(),(v).end()
#define eall(v) unique(all(v), v.end())
#define pb push_back
#define mp make_pair
#define fi first
#define se second
#define chmax(a, b) a = (((a)<(b)) ? (b) : (a))
#define chmin(a, b) a = (((a)>(b)) ? (b) : (a))
const int MOD = 1e9 + 7;
const int INF = 1e9;
const ll INFF = 1e18;

int R, C;
int X, Y;
int D, L;
const int MAX_N = 2000;
ll inv[MAX_N + 10];
ll fac[MAX_N + 10], facInv[MAX_N + 10];
class MATH{
public:
	MATH(){
		inverse();
		factroial();
	}
	ll nCk(ll n, ll k){// n! / k!*(n-k)!
		if(k < 0 || k > n) return 0;
		ll ret = fac[n];
		(ret *= facInv[k]) %= MOD;
		(ret *= facInv[n - k]) %= MOD;
		return ret;
	}
	ll nHk(ll n, ll k){// nHk = n+k-1 C k = (n+k-1)! / k! * (n-1)!
		if(n == 0 && k == 0) return 1;
		ll ret = fac[n + k - 1];
		(ret *= facInv[k]) %= MOD;
		(ret *= facInv[n - 1]) %= MOD;
		return ret;
	}
	ll nPk(ll n, ll k){//nPk = n! / (n-k)!
		if(k < 0 || k > n) return 0;
		ll ret = fac[n];
		(ret *= facInv[n - k]) %= MOD;
		return ret;
	}
private:
	void inverse(void){
		inv[1] = 1;
		for (int i = 2; i <= MAX_N; ++i){
			// inv[i] = MOD - (MOD / i) * inv[MOD % i] % MOD;
			inv[i] = inv[MOD % i] * (MOD - MOD / i) % MOD;
		}
	}
	void factroial(void){
		fac[0] = facInv[0] = 1;
		for (int i = 1; i <= MAX_N; ++i){
			fac[i] = (fac[i - 1] * i) % MOD;
			facInv[i] = (facInv[i - 1] * inv[i]) % MOD;
		}
	}
};
int main(void){
	cin >> R >> C >> X >> Y >> D >> L;
	MATH mt;
	ll ans = 0;
	for (int mask = 0; mask < (1<<4); ++mask){
		int x = X, y = Y;
		if(mask & (1<<0)) x--;
		if(mask & (1<<1)) y--;
		if(mask & (1<<2)) x--;
		if(mask & (1<<3)) y--;
		if(x < 0 || y < 0) continue;
		if(x * y < D + L) continue;
		int cnt = 0;
		rep(i, 4) if(mask & (1<<i))cnt++;
		// printf("%d %d\n", x, y);
		if(cnt % 2){ 
			// notans += mt.nCk(x * y, D + L) % MOD * fac[D + L] % MOD * facInv[D] % MOD * facInv[L] % MOD;
			ans -= mt.nCk(x * y, D) % MOD * mt.nCk(x * y - D, L) % MOD;
		}else{
			// notans -= mt.nCk(x * y, D + L) % MOD * fac[D + L] % MOD * facInv[D] % MOD * facInv[L] % MOD;
			ans += mt.nCk(x * y, D) % MOD * mt.nCk(x * y - D, L) % MOD;
		}
		ans = (ans + MOD) % MOD;
	}
	ll time = ((R - X + 1) * (C - Y + 1)) % MOD;
	ans = ans * time % MOD;
	printf("%lld\n", ans % MOD);
	return 0;
}

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