Snuke is standing on a two-dimensional plane. In one operation, he can move by 1 in the positive x-direction, or move by 1 in the positive y-direction.

Let us define a function f(r, c) as follows:

* f(r,c) :=  (The number of paths from the point (0, 0) to the point (r, c) that Snuke can trace by repeating the operation above)



Given are integers r_1, r_2, c_1, and c_2. Find the sum of f(i, j) over all pair of integers (i, j) such that r_1 ≤ i ≤ r_2 and c_1 ≤ j ≤ c_2, and compute this value modulo (10^9+7).

Constraints

* 1 ≤ r_1 ≤ r_2 ≤ 10^6
* 1 ≤ c_1 ≤ c_2 ≤ 10^6
* All values in input are integers.

Input

Input is given from Standard Input in the following format:


r_1 c_1 r_2 c_2


Output

Print the sum of f(i, j) modulo (10^9+7).

Examples

Input

1 1 2 2


Output

14


Input

314 159 2653 589


Output

602215194
#include <bits/stdc++.h>

using namespace std;

typedef long long	ll;
const int N = int(2e6 + 10);
ll fat[N];
const ll mod = ll(1e9 + 7LL);

ll fast_pow(ll number, ll x){
	ll b = number;
	ll r = 1LL;

	while(x){
		if(x & 1LL){
			r = (r * b) % mod;
		}

		b = (b * b) % mod;
		x >>= 1LL;
	}

	return r;
}

ll inv(ll number){
	return fast_pow(number, mod - 2LL);
}

ll comb(ll n, ll k){
	return ((fat[n] * inv(fat[k])) % mod * (inv(fat[n - k]))) % mod;
}

int main(){
	fat[0] = 1LL;

	for(ll i = 1LL ; i < N ; i++){
		fat[i] = (i * fat[i - 1]) % mod;
	}

	ll r1, c1, r2, c2;

	scanf("%lld %lld %lld %lld", &r1, &c1, &r2, &c2);

	ll sum = 0LL;

	for(ll c = c1 ; c <= c2 ; c++){
		sum += comb(r2 + c + 1, c + 1);

		if(sum >= mod){
			sum -= mod;
		}

		sum -= comb(r1 + c, c + 1);
		
		if(sum < 0){
			sum += mod;
		}
	}

	printf("%lld\n", sum);

	return 0;
}