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 <cstdio>
#include <vector>
#include <algorithm>

using namespace std;

const int MAX_S = 2000010;
const int MOD = 1000000007;
typedef long long Int;

Int fac[MAX_S + 1];
Int inv[MAX_S + 1], ifac[MAX_S + 1];

Int comb(int n, int r)
{
  Int ret = 1;
  ret = (ret * fac[n]) % MOD;
  ret = (ret * ifac[r]) % MOD;
  ret = (ret * ifac[n - r]) % MOD;
  return ret;
}

int main()
{
  int r1, r2, c1, c2;
  
  scanf("%d %d %d %d", &r1, &c1, &r2, &c2);
  
  int n = r2 + c2 + 1;
  
  inv[1] = 1;
  fac[0] = ifac[0] = 1;
  fac[1] = ifac[1] = 1;
  for (int i = 2; i <= n; i++) {
    fac[i] = (fac[i - 1] * i) % MOD;
    inv[i] = (inv[MOD % i] * (MOD - MOD / i)) % MOD;
    ifac[i] = ifac[i - 1] * inv[i] % MOD;
  }
  
  Int ans = 0;
  
  for (int i = r1; i <= r2; i++) {
    ans = (ans + comb(i + c2 + 1, c2)) % MOD;
    ans = (ans + MOD - comb(i + c1, c1 - 1)) % MOD;
  }
  
  printf("%lld\n", ans);
  
  return 0;
}
