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 long inv[1000002];

int C(int m, int n, int P) {
    long long res = 1;
    for (int i = 0; i < m; ++i) {
        res = res * (n - i) % P;
    }
    for (int i = 2; i <= m; ++i) {
        res = res * inv[i] % P;
    }
    return (int)res;
}

int main() {
    ios::sync_with_stdio(false);
    cin.tie(0);
    cout.tie(0);
    const int P = 1e9 + 7;
    inv[1] = 1;
    for (int i = 2; i <= 1000001; ++i) {
        inv[i] = (P - (P / i)) * inv[P % i] % P;
    }
    int r1, c1, r2, c2;
    cin >> r1 >> c1 >> r2 >> c2;
    int ans = (C(r2 + 1, r2 + 1 + c2 + 1, P) + C(r1, r1 + c1, P)) % P;
    ans = (ans + P - C(r2 + 1, r2 + 1 + c1, P)) % P;
    ans = (ans + P - C(r1, r1 + c2 + 1, P)) % P;
    cout << ans << endl;
    return 0;
}

