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;
const long MOD=1000000007;
long powmod(long x,long p){
  if(p==0)return 1;
  if(p%2)return x*powmod(x,p-1)%MOD;
  long tmp=powmod(x,p/2);return tmp*tmp%MOD;
}
long inv(long x){return powmod(x,MOD-2);}
long COM(long n,long k){
  long r=1;
  for(long i=0;i<k;i++){r=r*(n-i)%MOD;r=r*inv(i+1)%MOD;}
  return r;
}
long f(long r,long c){return COM(r+c,r);}
int main(){
  long r1,c1,r2,c2;cin>>r1>>c1>>r2>>c2;
  long ans=f(r2+1,c2+1)%MOD+(MOD-f(r2+1,c1))%MOD+(MOD-f(r1,c2+1))%MOD+f(r1,c1)%MOD;
  cout<<ans%MOD;
}