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>
#define LL long long
#define PII pair<int, int>
#define f first
#define s second 
using namespace std;
const LL INF = (LL) 1e9 + 5;
const LL MOD = (LL) 1e9 + 7;
const int MAXN = 2000005;

LL fac[MAXN], inv[MAXN];

LL C(LL n, LL k) {
	return fac[n] * inv[k] % MOD * inv[n - k] % MOD;
}

LL qpow(LL a, LL pw) {
	LL res = 1;
	while (pw) {
		if (pw & 1) res = res * a % MOD;
		a = a * a % MOD;
		pw >>= 1;
	}
	return res;
}

int main() {
	ios_base::sync_with_stdio(0); cin.tie(0);

	fac[0] = inv[0] = 1;
	for (int i = 1; i < MAXN; i++) {
		fac[i] = fac[i - 1] * i % MOD;
		inv[i] = qpow(fac[i], MOD - 2);
	}

	LL r1, c1, r2, c2, ans = 0;
	cin >> r1 >> c1 >> r2 >> c2;
	for (int i = r1; i <= r2; i++) {
		ans += C(i + c2 + 1, c2) - C(i + c1, c1 - 1);
	}
	
	cout << (ans % MOD + MOD) % MOD << '\n';
	
	return 0;
}