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<cstdio>
using namespace std;
const long long mod=1e9+7;
long long fac[20000010],inv[20000010],facinv[20000010];
int r1,c1,r2,c2;
long long C(int x,int y){
	++x;++y;
	return (fac[x+y]*facinv[x]%mod*facinv[y]%mod-1+mod)%mod;
}
int main(){
	inv[1]=fac[1]=facinv[1]=1ll;
	for (register int i=2;i<=2000005;++i){
		fac[i]=fac[i-1]*i%mod;
		inv[i]=(long long)(mod-mod/i)*inv[mod%i]%mod;
		facinv[i]=facinv[i-1]*inv[i]%mod;
	}
	scanf ("%d%d%d%d",&r1,&c1,&r2,&c2);
	printf ("%lld\n",(C(r2,c2)-C(r1-1,c2)+mod-C(r2,c1-1)+mod+C(r1-1,c1-1)+mod)%mod);
	return 0;
}