#include <bits/stdc++.h>
using namespace std;
using Int = long long;
const Int MAX = 2000010;
const Int MOD = 1000000007;
Int fac[MAX], finv[MAX], inv[MAX];
void COMinit() {
    fac[0] = fac[1] = 1;
    finv[0] = finv[1] = 1;
    inv[1] = 1;
    for (int i = 2; i < MAX; i++){
        fac[i] = fac[i - 1] * i % MOD;
        inv[i] = MOD - inv[MOD%i] * (MOD / i) % MOD;
        finv[i] = finv[i - 1] * inv[i] % MOD;
    }
}
Int COM(int n, int k) {
    if (n < k || n < 0 || k < 0) return 0;
    return fac[n] * (finv[k] * finv[n - k] % MOD) % MOD;
}
int main() {
    cin.tie(nullptr); ios::sync_with_stdio(false);
    COMinit();
    int r1, c1, r2, c2; cin >> r1 >> c1 >> r2 >> c2;
    cout << (COM(c1 + r1, c1) + MOD - COM(1 + c2 + r1, 1 + c2)
             + MOD - COM(1 + c1 + r2, c1) + COM(2 + c2 + r2, 1 + c2)) % MOD << endl;
    return 0;
}

### Prompt

Your task is to create a cpp solution to the following problem:

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

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
using Int = long long;
const Int MAX = 2000010;
const Int MOD = 1000000007;
Int fac[MAX], finv[MAX], inv[MAX];
void COMinit() {
    fac[0] = fac[1] = 1;
    finv[0] = finv[1] = 1;
    inv[1] = 1;
    for (int i = 2; i < MAX; i++){
        fac[i] = fac[i - 1] * i % MOD;
        inv[i] = MOD - inv[MOD%i] * (MOD / i) % MOD;
        finv[i] = finv[i - 1] * inv[i] % MOD;
    }
}
Int COM(int n, int k) {
    if (n < k || n < 0 || k < 0) return 0;
    return fac[n] * (finv[k] * finv[n - k] % MOD) % MOD;
}
int main() {
    cin.tie(nullptr); ios::sync_with_stdio(false);
    COMinit();
    int r1, c1, r2, c2; cin >> r1 >> c1 >> r2 >> c2;
    cout << (COM(c1 + r1, c1) + MOD - COM(1 + c2 + r1, 1 + c2)
             + MOD - COM(1 + c1 + r2, c1) + COM(2 + c2 + r2, 1 + c2)) % MOD << endl;
    return 0;
}

```