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>
const int Maxn=1000000;
const int Mod=1000000007;
int po[Maxn<<1|5];
int frac[Maxn<<1|5],inv_f[Maxn<<1|5];
int ksm(int a,int b){
	int ans=1;
	while(b){
		if(b&1){
			ans=1ll*ans*a%Mod;
		}
		b>>=1;
		a=1ll*a*a%Mod;
	}
	return ans;
}
int C(int n,int m){
	return 1ll*frac[n]*inv_f[m]%Mod*inv_f[n-m]%Mod;
}
int work(int n,int m){
	if(n>m){
		n^=m^=n^=m;
	}
	int ans=0;
	for(int i=0;i<=n;i++){
		ans=(ans+C(i+1+m,m))%Mod;
	}
	return ans;
}
int main(){
	frac[0]=inv_f[0]=1;
	for(int i=1;i<=(Maxn<<1)+1;i++){
		frac[i]=1ll*frac[i-1]*i%Mod;
	}
	inv_f[Maxn<<1|1]=ksm(frac[Maxn<<1|1],Mod-2);
	for(int i=(Maxn<<1);i>0;i--){
		inv_f[i]=1ll*inv_f[i+1]*(i+1)%Mod;
	}
	int r_1,r_2,c_1,c_2;
	scanf("%d%d%d%d",&r_1,&c_1,&r_2,&c_2);
	printf("%d\n",(((work(r_2,c_2)-work(r_1-1,c_2)+Mod)%Mod-work(r_2,c_1-1)+Mod)%Mod+work(r_1-1,c_1-1))%Mod);
	return 0;
}
