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 <algorithm>
#include <string.h>
#include <iostream>
#include <stdio.h>
using namespace std;

const long long mod = 1e9 + 7;

long long r1, r2, c1, c2;

long long power(long long m, long long k) {
	m %= mod;
	int res = 1;
	while (k) {
		if (k & 1) res = res * m % mod;
		m = m * m % mod;
		k >>= 1;
	}
	return res;
}

long long check(long long n, long long m) {
	if (n < m)
		return 0;

	long long res = 1;
	for (int i = 1; i <= m; i++)
		res = res * (n - i + 1) % mod * power(i, mod - 2) % mod;
	return res;
}

int main() {
	cin >> r1 >> c1 >> r2 >> c2;

	r2++, c2++;
	cout << (((check(r2 + c2, c2) - check(r1 + c2, c2) - check(r2 + c1, c1) + check(r1 + c1, c1)) % mod + mod) % mod) << endl;

	return 0;
}
