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 int long long
using namespace std;
constexpr int mod=1e9+7;
int fact[2000003];
int pow(int x,int n){
    int tmp=1;
    while(n){
        if(n&1)
            tmp=tmp*x%mod;
        x=x*x%mod;
        n>>=1;
    }
    return tmp;
}
int f(int r,int c){
    return fact[r+c]*pow(fact[r]*fact[c]%mod,mod-2)%mod;
}
signed main(){
    int r1,c1,r2,c2;
    cin>>r1>>c1>>r2>>c2;
    r2++,c2++;
    fact[0]=1;
    for(int i=1;i<=2000002;i++)
        fact[i]=i*fact[i-1]%mod;
    cout<<(f(r1,c1)-f(r1,c2)-f(r2,c1)+f(r2,c2)+mod*2)%mod<<endl;
}
