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>
#include <cstring>
using namespace std;
#define MOD 1000000007

long powMod(long x, long n, long mod){
	if (n == 0) return 1;
	else if (n == 1) return (x % mod);
	else if (n % 2 == 0){
		long t = powMod(x, n/2, mod);
		return (t*t) % mod;
	}
	else{
		return (x*powMod(x, n-1, mod)) % mod;
	}
}

long divMod(long a, long b, long mod){
	long t = powMod(b, mod-2, mod);
	return (a*t) % mod;
}

long r1, r2, c1, c2;
long sr1_c, sr2_c, ans;

int main(){
    cin >> r1 >> c1 >> r2 >> c2;
    sr1_c = r1;
    sr2_c = r2 + 1;
    ans = 0;
    for (int c = 0; c < c2; ++c){
        sr1_c = divMod((sr1_c*(r1 + c + 1)) % MOD, c + 2, MOD);
        sr2_c = divMod((sr2_c*(r2 + c + 2)) % MOD, c + 2, MOD);
        if (c >= c1 - 1){
            ans = (ans + sr2_c) % MOD;
            ans = (ans - sr1_c + MOD) % MOD;
        }
    }
    cout << ans;
}
