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;

typedef long long LL;
const int N = 2e6+7, M = 1e9+7;

LL fac[N],invfac[N];

LL power(LL a, LL p) {
    if (p==0)   return 1;
    LL ans = power(a, p/2);
    ans = (ans * ans)%M;
    if(p%2) ans = (ans * a)%M;
    return ans;
}

void pre() {
    fac[0]= 1;
    for (int i=1; i<N; i++) fac[i] = (fac[i-1] * i)%M;
    invfac[N-1] = power(fac[N-1], M-2);
    for (int i=N-2; i>=0; i--)      invfac[i] = (invfac[i+1] * (i+1))%M;
}

LL C(int n, int r) {
    if ( r< 0 || r> n)  return 0;
    LL num = fac[n];
    LL denom = (invfac[r] * invfac[n-r])%M;
    return (num * denom)%M;
}

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

    pre();
    int r1, c1, r2, c2;
    cin>>r1>>c1>>r2>>c2;
    r1--; c1--;

    LL ans = C(r2+c2+2, r2+1) - C(r1+c2+2, r1+1) - C(r2+c1+2, r2+1) + C(r1+c1+2, r1+1);
    ans = (ans % M + M)%M;
    cout<<ans<<endl;
}
