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 N = 2000006;
const int mod = 1e9+7;
int add(int a, int b) {
	return a + b >= mod ? a + b - mod : a + b;
}
int mul(int a, int b) {
	return int(1LL * a * b % mod);
}
int fexp(int b, int e = mod - 2) {
	int ans = 1;
	while(e) {
		if(e & 1) ans = mul(ans, b);
		b = mul(b, b);
		e /= 2;
	}
	return ans;
}

int fat[N], ifat[N];

int C(int n, int k) {
	if(n < k) return 0;
	return mul(mul(fat[n], ifat[k]), ifat[n - k]);
}

int main() {
	fat[0] = 1;
	for(int i = 1; i < N; i++) fat[i] = mul(i, fat[i - 1]);
	ifat[N - 1] = fexp(fat[N - 1]);
	for(int i = N - 2; i >= 0; i--) ifat[i] = mul(i + 1, ifat[i + 1]);

	int r1, c1, r2, c2;
	cin >> r1 >> c1 >> r2 >> c2;

	int ans = 0;
	
	for(int i = r1; i <= r2; i++) {
		int sum = add(C(i + c2 + 1, i + 1), mod - C(i + c1, i + 1));
		ans = add(ans, sum);
	}

	printf("%d\n", ans);
}
