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 <vector>
using namespace std;

//  a^b % m
long long powmod(long long a, long long b, long long m)
{
    long long r = 1;
    for (; b>0; b>>=1, a=a*a%m)
        if (b&1)
            r = r*a%m;
    return r;
}

int main()
{
    long long r1, c1, r2, c2;
    cin>>r1>>c1>>r2>>c2;

    long long M = 1000000007;
    vector<long long> F(2000002);
    F[0] = 1;
    for (int i=1; i<=2000001; i++)
        F[i] = F[i-1]*i%M;

    auto C = [&](long long x, long long y)
    {
        return F[x]*powmod(F[y], M-2, M)%M*powmod(F[x-y], M-2, M)%M;
    };

    long long ans = 0;
    for (long long r=r1; r<=r2; r++)
    {
        ans += C(r+c2+1, c2) - C(r+c1, c1-1);
        ans = (ans%M+M)%M;
    }
    cout<<ans<<endl;
}
