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>
#define N 2000005
using namespace std;

typedef long long ll;
ll M = 1e9 + 7;
ll r1, c1, r2, c2, fac[N] = {1, 1}, inv[N] = {1, 1}, fiv[N] = {1, 1};

ll s(ll p, ll q) {
	return (fac[p + q + 2] * fiv[p + 1] % M * fiv[q + 1] % M - 1 + M) % M;
}

int main()
{
	ll i;
	cin >> r1 >> c1 >> r2 >> c2;
	for (i = 2; i < N; i++) {
		fac[i] = fac[i - 1] * i % M;
		inv[i] = inv[M % i] * (M - M / i) % M;
		fiv[i] = fiv[i - 1] * inv[i] % M;
	}
    cout << (s(r2, c2) - s(r1 - 1, c2) - s(r2, c1 - 1) + s(r1 - 1, c1 - 1) + 2 * M) % M << endl;
    return 0;
}