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 <iostream>

using namespace std;
typedef long long ll;
const int MAX = 2000100;
ll inv[MAX],fact[MAX],fi[MAX];
constexpr ll mod = 1000000007;
void inverse(){
	int i;
	inv[1] = 1;
	for(i=2;i<MAX;i++){
		inv[i] = mod - (mod/i)*inv[mod%i]%mod;
	}
	fact[0] = fi[0] = 1;
	for(i=1;i<MAX;i++){
		fact[i] = fact[i-1]*i%mod;
		fi[i] = (fi[i-1]*inv[i])%mod;
	}
}

ll comb(int n,int k){
	if(n<0 || k<0 || n<k){
		return 0;
	}else{
		return fact[n]%mod*fi[k]%mod*fi[n-k]%mod;
	}
}

int main(){
	int r1,c1,r2,c2;
	cin >> r1 >> c1 >> r2 >> c2;
	inverse();
	long long ans;
	ans = comb(r2 + c2 + 2,r2 + 1) - comb(r1 + c2 + 1,r1) - comb(r2 + c1 + 1,c1) + comb(r1 + c1,r1);
	while(ans<0) ans += mod;
	ans %= mod;
	cout << ans << endl;
}