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;

const int mod = 1e9 + 7;
const int N = 3e6 + 123;
int	r1, r2, c1, c2, f[N], ans;

int mult(int a, int b)
{
	return 1ll * a * b % mod;
}

int add(int a, int b)
{
	a += b;
	if(a < 0) a += mod;
	if(a >= mod) a %= mod;
	return a;
}

int binpow(int w, int h)
{
	if(h == 0) return 1;
	if(h % 2 == 1) return mult(binpow(w, h - 1), w);
	else
	{
		int m = binpow(w, h / 2);
		return mult(m, m);
	}
}

int c(int n, int k)
{
	int num = f[n];
	int den = mult(f[k], f[n - k]);
	return mult(num, binpow(den, mod - 2));
}

int main()
{
	cin >> r1 >> c1 >> r2 >> c2;
	f[0] = 1;
	for(int i = 1; i <= 3e6; i++) f[i] = mult(f[i - 1], i);
	for(int i = r1; i <= r2; i++)
	{
		ans = add(ans, c(c2 + i + 1, c2));
		ans = add(ans, -c(i + c1, c1 - 1));
	}
	cout << ans % mod;
}