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>

#define MOD 1000000007
#define N 2222222

typedef long long ll;

ll fct[N] = { 1, 1 }, inv[N] = { 1, 1 }, fiv[N] = { 1, 1 };

ll combination(ll n, ll r)
{
	return fct[n] * fiv[r] % MOD * fiv[n - r] % MOD;
}

int main(void)
{
	ll r1, c1, r2, c2, i;

	scanf("%lld %lld %lld %lld" ,&r1, &c1, &r2, &c2);
	++r2, ++c2;

    for (i = 2; i <= r2+c2; i++)
	{
		fct[i] = fct[i - 1] * i % MOD;
		inv[i] = inv[MOD % i] * (MOD - MOD / i) % MOD;
		fiv[i] = fiv[i - 1] * inv[i] % MOD;
	}

	printf("%lld" ,(combination(r2 + c2, r2) - combination(r1 + c2, r1) - combination(r2 + c1, r2) + combination(r1 + c1, r1) + MOD * 2) % MOD);
	return 0;
}