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 fo(i,a,b) for(int i=(a);i<=(b);++i)
#define rv(i,a,b) for(int i=(a);i>=(b);--i)
using namespace std;
const int M = 2200000;
const int md=1e9+7;
typedef long long ll;
int n,m,k;
int fac[M],inv[M];
void ini(){
    inv[0] = inv[1] = 1;
    fac[0] = fac[1] = 1;
    fo(i,2,M-1) {
        inv[i] = 1ll*(md-md/i)*inv[md%i]%md;
    }
    fo(i,2,M-1) {
        inv[i] = 1ll*inv[i-1]*inv[i]%md;
        fac[i] = 1ll*fac[i-1]*i%md;
    }
}
ll C(int a,int b) {
    if(b<0 || a<b) return 0;
    return 1ll*fac[a]*inv[a-b]%md*inv[b]%md;
}
ll f(int a,int b) {
    return C(a+b,a);
}
int main(){
    ini();
    int r1,r2,c1,c2;
    cin>>r1>>c1>>r2>>c2;
    ll ans=f(r1,c1);
    fo(i,r1+1,r2)
        ans=(ans+f(i,c2))%md;
    fo(i,c1+1,c2)
        ans=(ans+f(r2,i))%md;
    cout<<ans<<endl;
    return 0;
}