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;

long long a, b, c, d, m = 0;
const long long M = 1e9 + 7;
long long g[2000003], h[2000003];

long long pow(long long p, long long q) {
	long long r = 1, s = p;

	while (q) {
		if (q & 1)
			r = r * s % M;

		s = s * s % M;
		q >>= 1;
	}

	return r;
}

int main()
{
	cin >> a >> b >> c >> d;

	g[1] = 1;
	h[1] = 1;

	for (long long i = 2; i <= c + d + 2; i++) {
		g[i] = g[i - 1] * i % M;
		h[i] = pow(g[i], M - 2);
	}

	m = (g[c + d + 2] * h[c + 1] % M) * h[d + 1] % M;
	m = (m + (g[a + b] * h[a] % M) * h[b] % M) % M;
	m = (m + M - (g[b + c + 1] * h[b] % M) * h[c + 1] % M) % M;
	m = (m + M - (g[a + d + 1] * h[a] % M) * h[d + 1] % M) % M;

	cout << m << endl;
}
