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 <stdio.h>
#define N 2222222
#define M 1000000007
typedef long long LL;

LL f[N];

LL qpow(LL x, int y)
{
	if(!y) return 1;
	LL t = qpow(x, y >> 1);
	t = t * t % M;
	if(y & 1) t = t * x % M;
	return t;
}

LL S(int x, int y)
{
	LL ans = f[x + y + 2];
	ans = ans * qpow(f[y + 1], M - 2) % M;
	ans = ans * qpow(f[x + 1], M - 2) % M;
	return ans - 1;
}

int main() 
{
	int r1, c1, r2, c2, m, i, j;
	LL sum;
		
	scanf("%d%d%d%d", &r1, &c1, &r2, &c2);
	m = r2 + c2 + 2;
	for(i = 2, f[0] = f[j = 1] = 1; i <= m; j = i++){
		f[i] = f[j] * (LL)i % M;
	}
	sum = S(r2, c2) - S(r1 - 1, c2);
	if(sum < 0) sum += M;
	sum -= S(r2, c1 - 1);
	if(sum < 0) sum += M;
	sum += S(r1 - 1, c1 - 1);
	if(sum >= M) sum -= M;
	printf("%lld\n", sum);
		
	return 0;
}