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;
typedef long long ll;

ll fact_pow(ll n,ll m,ll p)
{
  ll res=1;
  for(ll i=n;i>=1;i--)
  {
    res=res*i%m;
  }
  
  ll ans=1;
  while(p>0)
  {
    if(p&1)ans=ans*res%m;
    res=res*res%m;
    p>>=1;
  }

return ans;
}



int main()
{
  ll i ,j,r1,r2,c1,c2,m=1000000007,temp1=1,ans=0,temp2,temp3,temp4,temp5;
  cin>>r1>>c1>>r2>>c2;
  
temp1=fact_pow(r2+c2+2,m,1)*fact_pow(r2+1,m,m-2)%m;
temp1=temp1*fact_pow(c2+1,m,m-2)%m;



temp2=fact_pow(r2+c1+1,m,1)*fact_pow(r2+1,m,m-2)%m;
temp2=temp2*fact_pow(c1,m,m-2)%m;

temp3=fact_pow(r1+c2+1,m,1)*fact_pow(r1,m,m-2)%m;
temp3=temp3*fact_pow(c2+1,m,m-2)%m;

temp4=fact_pow(r1+c1,m,1)*fact_pow(r1,m,m-2)%m;
temp4=temp4*fact_pow(c1,m,m-2)%m;

ans=temp1+temp4-temp2-temp3;


cout<<(ans+4*m)%m<<endl;

return 0;

}