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;

typedef long long int64;
const int MAX = 2e6 + 5;
const int MOD = 1e9 + 7;
int r1, c1, r2, c2;
int64 f[MAX], inv[MAX];

int64 exp(int64 a, int64 n) {
	int64 ans = 1;
	while(n > 0) {
		if(n % 2LL == 1LL)
			ans = ans * a % MOD;
			
		a = a * a % MOD;
		n /= 2LL;
	}
	
	return ans;
}

int64 comb(int n, int k) {
	return f[n] * inv[k] % MOD * inv[n - k] % MOD;
}

int64 s(int x, int y) {
	int64 ans = 0;
	for(int i = 1; i <= y + 1; i++)
		ans = (ans + comb(i + x, x)) % MOD;

	return ans;
}

int main() {
	scanf("%d%d%d%d", &r1, &c1, &r2, &c2);

	f[0] = inv[0] = 1;
	for(int i = 1; i <= (int) 2e6 + 4; i++) {
		f[i] = 1LL * f[i - 1] * i % MOD;
		inv[i] = exp(f[i], MOD - 2);
	}

	int64 ans = (s(r2, c2) - s(r2, c1 - 1) + MOD) % MOD;
	ans = (ans - s(r1 - 1, c2) + MOD) % MOD;
	ans = (ans + s(r1 - 1, c1 - 1)) % MOD;

	printf("%lld\n", ans);
	return 0;
}