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 int nmax=2e6+5;
const int mod=1e9+7;
int fact[nmax+1],invfact[nmax+1];
int modpow(int x,int y){
  int ans=1;
  while(y){
   if(y&1)ans=(1LL*ans*x)%mod;
   x=(1LL*x*x)%mod;
   y>>=1;
  }
  return ans;
}
int nCr(int n,int r){
  if(r>n)return 0;
  return (1LL*( (1LL*fact[n]*invfact[r])%mod )*invfact[n-r])%mod;
}  
void preprocess(){
 fact[0]=1;
 for(int i=1;i<=nmax;i++){
   fact[i]=(1LL*i*fact[i-1])%mod;
 }
 invfact[nmax]=modpow(fact[nmax],mod-2);
 for(int i=nmax-1;i>=0;i--){
   invfact[i]=(1LL*(i+1)*invfact[i+1])%mod;
 }
}  
int main()
{
  int r1,c1,r2,c2;
  cin>>r1>>c1>>r2>>c2;
  preprocess();
  long long ans=0;
  for(int i=r1;i<=r2;i++){
    ans+=nCr(i+c2+1,i+1);
    ans-=nCr(i+c1,i+1);
    ans=(ans+mod)%mod;
  }
  cout<<ans<<"\n";
}
