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>
#include<algorithm>
#define ll long long
using namespace std;
const int N=2022202;
int fac[N],ifac[N];
int p=1e9+7;
ll ans=0;
ll power(int a,int b){
	int sum=1;
	for (; b; b>>=1){
		if (b&1)	sum=1ll*sum*a%p;
		a=1ll*a*a%p;
	}
	return sum;
}
ll C(int n,int m){return 1ll*fac[n]*ifac[m]%p*ifac[n-m]%p;}
ll calc(int n,int m){
	if (n<0||m<0)	return 0;
	ll sum=0;
	for (int i=1; i<=n+1; i++)
		sum=(sum+C(i+m,i))%p;
	return sum%p;
}

int main(){
	int n1,m1,n2,m2;
	scanf("%d%d%d%d",&n1,&m1,&n2,&m2);
	int n=n2+m2+1;
	ifac[0]=fac[0]=1;
	for (int i=1; i<=n; i++)	fac[i]=1ll*fac[i-1]*i%p;
	ifac[n]=power(fac[n],p-2);
	for (int i=n-1; i>=1; i--)	ifac[i]=1ll*ifac[i+1]*(i+1)%p;
	ll ans=calc(n2,m2)-calc(n2,m1-1)-calc(n1-1,m2)+calc(n1-1,m1-1);
	printf("%lld\n",(ans%p+p)%p);
	return 0;
}