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>
using namespace std;
int a[20000011],p=1000000007;
int pow1(int rarac,int d){
  long long c; 
  if(d==1)
    return rarac;
  else{
    c=pow1(rarac,d/2);
    if(d%2==0){
      c*=c;
      c%=p;
    }
    else{
      c*=c;
      c%=p;
      c=c*rarac;
      c%=p;
    }
  }
  return c;
}
int jandaba(int n,int m){
  long long  A=a[n+m];
  long long B=((long long)a[n]*a[m])%p;
  return (A * pow1(B,p-2))%p;
}
int datvla(int x,int y){
  long long k=0;
    k+=jandaba(x+1,y+1);
    k%=p;
  return k;
}
int main() {
  int r1,c1,r2,c2;
  long long ans=0;
  cin>>r1>>c1>>r2>>c2;
  long long x=1;
  for(int i=1;i<=2000010;i++){
    x*=i;
    x%=p;
    a[i]=x;
  }
  a[0]=1;
  ans+=datvla(r2,c2);
  ans%=p;
  ans-=datvla(r1-1,c2);
  ans%=p;
  ans-=datvla(r2,c1-1);
  ans%=p;
  ans+=datvla(r1-1,c1-1);
  ans%=p;
  cout<<(ans+p)%p;
}