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<iostream>
using namespace std;
long mod=1e9+7;
long F[2<<20],I[2<<20];
long power(long a,long b){return b?power(a*a%mod,b/2)*(b%2?a:1)%mod:1;}
long f(int R,int C)
{
	long ret=0;
	for(long c=0;c<=C;c++)
	{
		(ret+=F[c+R+1]*I[c+1]%mod*I[R]%mod)%=mod;
	}
	return ret;
}
int main()
{
	F[0]=1;
	for(long i=1;i<2<<20;i++)F[i]=F[i-1]*i%mod;
	I[(2<<20)-1]=power(F[(2<<20)-1],mod-2);
	for(long i=(2<<20)-1;i--;)I[i]=I[i+1]*(i+1)%mod;
	int r1,c1,r2,c2;
	cin>>r1>>c1>>r2>>c2;
	long ans=f(r1-1,c1-1)-f(r2,c1-1)-f(r1-1,c2)+f(r2,c2);
	ans=(ans%mod+mod)%mod;
	cout<<ans<<endl;
}
