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>
#include<cstdint>

int64_t const MOD = 1e9+7;

int64_t const MAXRC = 1e6;
int const MAXN = (MAXRC+1)*2;

int64_t inv[MAXN+1];
int64_t fact[MAXN+1];
int64_t ifact[MAXN+1];

void init(int n) {
  fact[0] = ifact[0] = fact[1] = ifact[1] = inv[1] = 1;
  for(int64_t i = 2; i <= n; ++i) {
    fact[i] = fact[i-1]*i%MOD;
    inv[i] = (MOD/i)*(MOD - inv[MOD%i])%MOD;
    ifact[i] = ifact[i-1]*inv[i]%MOD;
  }
}

int64_t f(int r, int c) {
  int64_t res = fact[r+c+2]*ifact[r+1]%MOD;
  (res *= ifact[c+1]) %= MOD;
  (res += MOD-1) %= MOD;
  return res;
}

int main() {
  int r1, c1, r2, c2;
  std::cin >> r1 >> c1 >> r2 >> c2; --r1; --c1;
  init(r2+c2+2);
  int64_t ans = (f(r2, c2) + f(r1, c1))%MOD, mi = (f(r1, c2) + f(r2, c1))%MOD;
  (ans += MOD - mi) %= MOD;
  std::cout << ans << std::endl;
  return 0;
}
