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;

typedef long long int ll;

const int N = 2e6 + 5;
const int mod = 1e9 + 7;

vector < ll > fact (N);

ll pwr (ll a, ll b) {
  ll res = 1;
  while (b > 0) {
    if (b & 1) res = (res * a) % mod;
    a = (a * a) % mod;
    b >>= 1;
  }
  return res;
}

ll inv (ll a) {
  return pwr (a, mod - 2);
}

ll nCr (int n, int r) {
  return ((((fact[n] * inv (fact[r])) % mod) * inv (fact[n - r])) % mod);
}

ll f (int i, int j) {
  return nCr (i + j, j);
}

ll g (int i, int j) {
  return (f (i + 1, j + 1) - 1 + mod) % mod;
}

int main () {
  ios_base::sync_with_stdio(false);
  cin.tie(0);cout.tie(0);

  fact[0] = 1;
  for (int i = 1; i < N; i++) fact[i] = (i * fact[i - 1]) % mod;

  int r1, c1, r2, c2;
  cin >> r1 >> c1 >> r2 >> c2;

  ll ans = (g (r2, c2) - g (r2, c1 - 1) - g (r1 - 1, c2) + g (r1 - 1, c1 - 1) + 2 * mod) % mod;

  cout << ans << '\n';
}
