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 long long long
using namespace std;
const int N=4e6,mod=1e9+7;
int big(int b,int p,int m=mod)
{
  int ret=1;
  while(p){if(p&1)ret=(1LL*ret*b)%m;b=(1LL*b*b)%m;p/=2;}
  return ret;
}
int fac[N+2];
void init(int n)
{
  fac[0]=1;
  for(int i=1;i<=n;i++)fac[i]=(1LL*fac[i-1]*i)%mod;
}
int ncr(int n,int r)
{
  int a=fac[n];a=(1LL*a*big(fac[r],mod-2))%mod;
  return (1LL*a*big(fac[n-r],mod-2))%mod;
}
int main()
{
  ios_base::sync_with_stdio(0);cin.tie(0);
  init(N);

  int r1,c1,r2,c2;cin>>r1>>c1>>r2>>c2;

  int ans=0;
  for(int c=c1;c<=c2;c++)
  {
    ans=(ans+ncr(r2+c+1,r2))%mod;
    ans=((ans-ncr(r1+c,r1-1))%mod+mod)%mod;
  }
  cout<<ans<<endl;
  
  return 0;
}