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;
const int mod=1000000007;
int p(int A,int B){
  if(!B)return 1;
  if(B&1)return p(A,B-1)*A%mod;
  int C=p(A,B/2);
  return C*C%mod;
}
int k[2000100];
int C(int A,int B){
  return k[A+B]*p(k[A]*k[B]%mod,mod-2)%mod;
}
signed main(){
  k[0]=1;
  for(int i=1;i<=2000002;i++)k[i]=k[i-1]*i%mod;
  int a,b,c,d;
  cin>>a>>b>>c>>d;
  c++,d++;
  cout<<(C(c,d)+C(a,b)-C(a,d)-C(c,b)+mod*2)%mod<<endl;
}