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;
static const int64_t mod=1000000007;
int64_t f(int64_t x,int64_t y){
if(y==0)
  return 1;
  else if(y%2==0)
    return (f(x,y/2)*f(x,y/2))%mod;
  else
    return (x*((f(x,y/2)*f(x,y/2))%mod))%mod;
}
int64_t comb(int64_t n,int64_t k){
int64_t a=1;
  for(int64_t i=1;i<=k;i++){
  a=(a*(n+1-i))%mod;
    a=(a*f(i,mod-2))%mod;
  }return a;
}
int main(){
  int64_t r1,c1,r2,c2;
  cin>>r1>>c1>>r2>>c2;
  int64_t ans=(comb(r2+c2+2,r2+1)+comb(r1+c1,r1)-comb(r2+c1+1,c1)-comb(r1+c2+1,r1)+2*mod)%mod;
  cout<<ans<<endl;
  return 0;
}