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>

const int mod = 1e9 + 7;
const int N = 3e6;

using int64 = long long;

int64 fac[N], ifac[N];

int64 binom(int n, int m) {
  return fac[n] * ifac[m] % mod * ifac[n - m] % mod;
}

int64 pow_mod(int64 a, int64 n) {
  int64 r = 1;
  for (; n; n >>= 1) {
    if (n & 1) r = r * a % mod;
    a = a * a % mod;
  }
  return r;
}

int main() {
  int r1, r2, c1, c2;
  scanf("%d%d%d%d", &r1, &c1, &r2, &c2);
  fac[0] = ifac[0] = 1;
  for (int i = 1; i <= r2 + c2 + 1; ++i) {
    fac[i] = fac[i - 1] * i % mod;
    ifac[i] = pow_mod(fac[i], mod - 2);
  }
  int64 ret = 0;
  for (int n = r1; n <= r2; ++n) {
    ret += binom(n + c2 + 1, c2) - binom(n + c1, c1 - 1);
  }
  ret %= mod; ret += mod; ret %= mod;
  printf("%lld\n", ret);
  return 0;
}
