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
#define inf 1000000007
using namespace std;
ll sum[2000009];
ll pow1(ll x,ll y)
{
    ll res=1;
    while(y)
    {
        if(y%2)
            res=res*x%inf;
        x=x*x%inf;
        y/=2;
    }
    return res;
}
ll inv(ll x)
{
    return pow1(x,inf-2);
}
int main()
{
    int a,b,c,d;
    ll tmp,tmp1;
    sum[0]=1;
    scanf("%d%d%d%d",&a,&b,&c,&d);
    for(int i=1;i<=2000008;i++)
        sum[i]=sum[i-1]*(ll)(i)%inf;
    tmp=(sum[c+d+2]*inv(sum[d+1])%inf*inv(sum[c+1])%inf+sum[a+b]*inv(sum[a])%inf*inv(sum[b])%inf)%inf;
    tmp1=(sum[a+d+1]*inv(sum[d+1])%inf*inv(sum[a])%inf+sum[c+b+1]*inv(sum[b])%inf*inv(sum[c+1])%inf)%inf;
    printf("%lld",(tmp-tmp1+inf)%inf);
    return 0;
}
