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 N = 1e6 + 10 ;
typedef long long ll ;
const int mod = 1e9 + 7 ;
ll qmi(ll a , ll b)
{
  ll res =1 ;
  while(b)
   {
     if(b & 1) res = res * a % mod ;
     a = a * a % mod ;
     b >>= 1 ;
   }
   return res ;
}
ll get(ll n , ll m)
{
   ll res = 1 , ans = 1 ;
   n ++ , m ++ ;
   n += m ;
   for(int i = 1; i <= m ;i ++)
    res = res * i % mod , ans = ans * (n - i + 1) % mod ;
  return ans * qmi(res , mod - 2) % mod - 1 ;
}
int main()
{
  int r1 , r2 , c1 , c2 ;
  cin >> r1 >> c1 >> r2 >> c2 ;
  cout << ((get(r2 , c2) - get(r2 , c1 - 1) + mod - get(r1 - 1 , c2)  + mod + get(r1 - 1 , c1 - 1) % mod + mod ) % mod + mod )% mod << endl ;
  return 0 ;
}
