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>
using ll = long long;
using namespace std;
constexpr ll MOD = 1e9 + 7;
constexpr int MAX = 2000020;
ll fac[MAX], inv[MAX], finv[MAX];

ll comb(int n, int k) {
	return (fac[n] * finv[n - k] % MOD) * finv[k] % MOD;
}

int r1, r2, c1, c2;

int main()
{
	cin >> r1 >> c1 >> r2 >> c2;
	fac[0] = inv[0] = finv[0] = 1;
	fac[1] = inv[1] = finv[1] = 1;
	for (int i = 2; i < MAX; ++i) {
		fac[i] = fac[i - 1] * i % MOD;
		inv[i] = MOD - inv[MOD % i] * (MOD / i) % MOD;
		finv[i] = finv[i - 1] * inv[i] % MOD;
	}

	cout << (comb(r2 + c2 + 2, c2 + 1) - comb(r1 + c2 + 1, c2 + 1) - comb(r2 + c1 + 1, c1) + comb(r1 + c1, c1) + MOD) % MOD;
	return 0;
}