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;

vector<long long> F, RF, R;
long long MOD = 1000000007;

void init(long long N) {
	F.resize(N + 1);
	RF.resize(N + 1);
	R.resize(N + 1);
	F[0] = F[1] = RF[0] = RF[1] = R[0] = R[1] = 1;
	for (int i = 2; i <= N; i++) {
		F[i] = (F[i - 1] * i) % MOD;
		R[i] = MOD - (R[MOD % i] * (MOD / i)) % MOD;
		RF[i] = (RF[i - 1] * R[i]) % MOD;
	}
}

long long Comb(long long N, long long M) {
	return (F[N] * ((RF[N - M] * RF[M]) % MOD)) % MOD;
}

int main() {
	long long R1, C1, R2, C2;
	cin >> R1 >> C1 >> R2 >> C2;
	R2++, C2++;
	init(2000010);
	long long ANS = 0;
	ANS += Comb(R1 + C1, R1) - 1;
	ANS += Comb(R2 + C2, R2) - 1;
	ANS -= Comb(R1 + C2, R1) - 1;
	ANS -= Comb(R2 + C1, R2) - 1;
	ANS += MOD * 2;
	cout << ANS % MOD << endl;
}