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 int64_t mod = 1000000007;
vector<int64_t> fact, inv;

int64_t power(int64_t n, int64_t k) {
  if (k == 0) return 1;
  int64_t ans = power(n * n % mod, k / 2);
  if (k % 2) ans = ans * n % mod;
  return ans;
}

void init(int n) {
  fact.push_back(1);
  inv.push_back(1);
  for (int i = 1; i <= n; i++) {
    fact.push_back(fact.at(i - 1) * i % mod);
    inv.push_back(power(fact.at(i), mod - 2));
  }
}

int64_t ncr(int64_t n, int64_t r) {
  return fact.at(n) * inv.at(r) % mod * inv.at(n - r) % mod;
}

int main() {
  int64_t r1, c1, r2, c2;
  cin >> r1 >> c1 >> r2 >> c2;
  r2++; c2++;
  init(r2 + c2);
  cout << (ncr(r2 + c2, r2) + ncr(r1 + c1, r1) - ncr(r2 + c1, r2) - ncr(r1 + c2, r1) + 2 * mod) % mod << endl;
}
