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 <iostream>

using namespace std;

const int M = 1e9+7;

long long kaijo[2000005];

int mpow(long long a, int n)
{
  if (n % 2) return mpow(a, n - 1) * a % M;
  if (n == 0) return 1;
  return mpow(a * a % M, n / 2);
}

long long cmb(int n, int r)
{
  return kaijo[n] * mpow(kaijo[r], M-2) % M * mpow(kaijo[n-r], M-2) % M;
}

int main()
{
  int r, c, R, C; cin >> r >> c >> R >> C;
  
  kaijo[0] = 1;
  for (int i = 1; i < 2000005; ++i)
    kaijo[i] = kaijo[i-1] * i % M;
  
  int ans = (cmb(R+C+2, C+1)-cmb(R+c+1, c)-cmb(C+r+1, C+1)+cmb(r+c, c)+M*2) % M;
  cout << ans << endl;
}