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>
#define LL long long
using namespace std;

const int MAXN = 2e6+10;
const int P = 1e9+7;

LL fac[MAXN];
LL invf[MAXN];

LL fp(LL a, LL n){
    if(n==0)
        return 1;

    LL h = fp(a, n/2);
    h *= h;
    h %= P;
    if(n&1){
        h = h*a %P;
    }

    return h;
}


LL C(LL a, LL b){
    return fac[a] * invf[a-b] % P * invf[b] %P;
}
int main(){
    int r1, c1, r2, c2;
    cin >>r1>>c1>>r2>>c2;

    fac[0] = 1;
    fac[1] = 1;
    invf[0] = 1;
    invf[1] = 1;

    for(int i=2;i<=(int)2e6+1;i++){
        fac[i] = fac[i-1] * i %P;
        invf[i] = fp(fac[i], P-2);
    }

    LL ans = 0;

    for(int i=r1;i<=r2;i++){
        ans += C(i+c2+1, c2) - C(i+c1, c1-1);
        ans %=P;
    }

    if(ans<0)
        ans+=P;
    cout<<ans;

}
