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>
#include <cstdio>
using namespace std;
typedef long long ll;

ll r1, c1, r2, c2, M=1e9+7;

ll pow(ll p, ll q) {
	if(q==0) return 1;
	ll t = pow(p, q/2);
	return t * t % M * (q%2 ? p : 1) % M;
}

ll C(ll p, ll q) {
	ll x=1, y=1;
	for(ll i=0; i<q; i++) {
		x = x * (p-i) % M;
		y = y * (i+1) % M;
	}
	return x * pow(y, M-2) % M;
}

int main() {
	cin >> r1 >> c1 >> r2 >> c2;
	r2++; c2++;
	cout << (C(r2+c2, r2) - C(r2+c1, c1) - C(r1+c2, r1) + C(r1+c1, r1) + 2*M) % M;
	return 0;
}