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 <stdio.h>
typedef long long ll;
ll dp[3000001]={1,};
const ll M = 1000000007;
ll inverse(ll x){
	ll ret = 1;
	for(int i=0;i<31;i++){
		if((M-2)&(1LL<<i)){
			ret=(ret*x)%M;
		}
		x=(x*x)%M;
	}
	return ret;
}
ll f(int a, int b){
	ll ret = dp[a+b];
	ret=(ret*inverse(dp[a]))%M;
	ret=(ret*inverse(dp[b]))%M;
	return ret;
}
ll g(int a, int b){
	return (f(a+1,b+1)+M-1)%M;
}
int main(){
	for(int i=1;i<=3000000;i++) dp[i] = (dp[i-1]*i)%M;
	int r1,c1,r2,c2;
	scanf("%d %d %d %d",&r1,&c1,&r2,&c2);
	printf("%lld",(2*M+g(r2,c2)-g(r1-1,c2)-g(r2,c1-1)+g(r1-1,c1-1))%M);
}