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;

long inv(int a, int m) {
    long i = 1, j = 0;
    for(int b = m; a > 1; swap(i, j), swap(a, b)) {
        j = (j + b / a * (m - i)) % m;
        b %= a;
    }
    return i;
}
int p = 1e9 + 7;
long f[2222222] = {1};
long co(int a, int b) { return f[a + b] * inv(f[a] * f[b] % p, p) % p; }
int main() {
    int r, c, s, d;
    cin >> r >> c >> s >> d;
    for(int i = 0; i < s + d + 3; i++)
        f[i + 1] = f[i] * (i + 1) % p;
    cout << (co(s + 1, d + 1) + co(r, c) + p - co(s + 1, c) + p -
             co(r, d + 1)) %
                p
         << endl;
    return 0;
}
