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;

#define ll long long
#define ar array

const int mxN=1e6, M=1e9+7;
int r1, r2, c1, c2;
ll iv[3*mxN], f1[3*mxN], f2[3*mxN];

ll nck(int n, int k) {
	return f1[n]*f2[k]%M*f2[n-k]%M;
}

int main() {
	ios::sync_with_stdio(0);
	cin.tie(0);

	iv[1]=1;
	for(int i=2; i<3*mxN; ++i)
		iv[i]=M-M/i*iv[M%i]%M;
	f1[0]=f2[0]=1;
	for(int i=1; i<3*mxN; ++i) {
		f1[i]=f1[i-1]*i%M;
		f2[i]=f2[i-1]*iv[i]%M;
	}
	cin >> r1 >> c1 >> r2 >> c2;
	//cout << nck(r2+c2+2, c2+1) << " " << nck(r1+c2+1, c2+1) << " " << nck(r1+c1, c1) << endl;
	cout << ((nck(r2+c2+2, c2+1)-nck(r1+c2+1, c2+1)-nck(r2+c1+1, c1)+nck(r1+c1, c1))%M+M)%M;
}