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<bits/stdc++.h>
using namespace std;
typedef long long ll;
ll x1,x2,a1,a2,MOD=1000000007,bik[2000003],ans;
ll f(ll x,ll y){
    if(y==1)return x;
    if(y%2==1)return f(x,y-1)*x%MOD;
    else return f(x,y/2)*f(x,y/2)%MOD;
}
ll comb(ll x,ll y){
    return bik[x+y]*f(bik[y],MOD-2)%MOD*f(bik[x],MOD-2)%MOD;
}
int main(void){
    cin>>x1>>a1>>x2>>a2;
    bik[0]=1;
    for(ll i=1;i<=2000002;i++){
        bik[i]=bik[i-1]*i%MOD;
    }
    ans=comb(a2+1,x2+1)-comb(x2+1,a1)-comb(a2+1,x1)+comb(a1,x1);
    ans%=MOD;
    ans=(ans+MOD)%MOD;
    cout<<ans<<endl;
}
