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<bits/stdc++.h>
using namespace std;

const int MOD = 1e9+7;

int r1, r2, c1, c2;

int ksm(long long x,long long y)
{
	x %= MOD;
	long long rt = 1LL;
	while ( y )
	{
		if ( y & 1 )
			rt = rt * x % MOD;
		x = x * x % MOD;
		y >>= 1;
	}
	return (int)rt;
}

int C(int n,int m)
{
	if ( n < m )
		return 0;
	long long rt = 1LL;
	for ( int i = 0 ; i < m ; i++ )
		rt = rt * (long long)(n-i) % (long long)MOD * (long long)ksm(i+1,MOD-2) % (long long)MOD;
	return (int)rt;
}

int u(int x,int y)
{
	return C(x+y,min(x,y));
}

int s(int x,int y)
{
	return u(y+1,x+1)-1;
}

int main()
{
	scanf("%d%d%d%d",&r1,&c1,&r2,&c2);
	printf("%d",(s(r2,c2)-s(r2,c1-1LL)-s(r1-1LL,c2)+s(r1-1LL,c1-1LL)+MOD)%MOD);
	printf("\n");
	return 0;
}