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>
#define MOD 1000000007

using namespace std;
typedef long long ll;

ll exp(ll x,ll p){
    if(p==0)
        return 1LL;
    ll y=exp(x,p/2);
    if(p%2==0)
        return (y*y)%MOD;
    return (((y*y)%MOD)*x)%MOD;
}

ll f[2000005];
ll inv[2000005];

ll g(ll x,ll y){
    return (((((f[x+y+2]*inv[x+1])%MOD)*inv[y+1])%MOD)+MOD-1)%MOD;
}

ll i;
ll c1,c2,r1,r2;

int main()
{
    f[0]=1;
    inv[0]=1;
    for(i=1;i<=2000002;i++){
        f[i]=f[i-1]*i%MOD;
        inv[i]=exp(f[i],MOD-2);
    }
    cin>>r1>>c1>>r2>>c2;
    cout<<(MOD + g(r2,c2) - g(r2,c1-1) - g(r1-1,c2) + g(r1-1,c1-1))%MOD<<'\n';
    return 0;
}
