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 <algorithm>

#define MOD 1000000007

using namespace std;

long long modinv(long long a, long long m) {
    long long b = m, u = 1, v = 0;
    while (b) {
        long long t = a / b;
        a -= t * b; swap(a, b);
        u -= t * v; swap(u, v);
    }
    u %= m;
    if (u < 0) u += m;
    return u;
}

long g(int r, int c){
    long ans = 0;
    long a = c+1;
    for(long i=0; i<r+1; i++){
        ans += a;
        ans %= MOD;
        a *= (c + i + 2);
        a %= MOD;
        a *= modinv(i+2, MOD);
        a %= MOD;
    }
    return ans;
}


int main(){
    int r1, c1, r2, c2;
    cin >> r1 >> c1 >> r2 >> c2;
    long ans = 0;
    cout << (g(r2, c2) - g(r1-1, c2) - g(r2, c1-1) + g(r1-1, c1-1) + MOD) % MOD << endl;
    return 0;
}