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;

const int mod = (int) 1e9 + 7;

long long fact[2000006], mmi[2000006];

long long power(long long N, long long expo)
{
    long long ans = 1;

    while(expo)
    {
        if(expo % 2)
            ans = ans * N % mod;
        
        N = N * N % mod;
        expo /= 2;
    }

    return ans;
}

long long nCr(int N, int r)
{
    if(N < r)
        return 0;
    
    return fact[N] * mmi[r] % mod * mmi[N-r] % mod;
}

int main() {
    ios::sync_with_stdio(0);
    cin.tie(NULL), cout.tie(NULL);

    int r1, c1, r2, c2;
    cin >> r1 >> c1 >> r2 >> c2;

    fact[0] = mmi[0] = 1;

    for(int i=1; i<=2000001; i++)
    {
        fact[i] = fact[i-1] * i % mod;
        mmi[i] = power(fact[i], mod-2);
    }

    long long ans = 0;

    for(int r = r1; r <= r2; r++)
        ans += nCr(r+c2+1, r+1) + mod - nCr(r+c1, r+1);

    cout << ans % mod << "\n";
    return 0;
}
