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 long mod = 1000000007;
long fact(long n) {
  return n == 0 ? 1 : n * fact(n - 1) % mod;
}

long mpow(long b, long e) {
  if (e == 0) return 1;
  if (e % 2 == 1) return b * mpow(b, e - 1) % mod;
  long t = mpow(b, e / 2);
  return t * t % mod;
}

long inv(long n) {
  return mpow(n, mod - 2);
}

long sub(int m, int n) {
  return fact(m + n) * inv(fact(m) * fact(n) % mod) % mod;  
}

int main() {
  int a, b, c, d;
  cin >> a >> b >> c >> d;
  long sum = (
    sub(a, b)
    - sub(a, d + 1)
    - sub(c + 1, b)
    + sub(c + 1, d + 1)
    + 4 * mod
    ) % mod;
  cout << sum << endl;
}