Problem:
Score : 600 points

Problem Statement

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).

Sample Input 1

1 1 2 2

Sample Output 1

14

For example, there are two paths from the point (0, 0) to the point (1, 1): (0,0) → (0,1) → (1,1) and (0,0) → (1,0) → (1,1), so f(1,1)=2.

Similarly, f(1,2)=3, f(2,1)=3, and f(2,2)=6. Thus, the sum is 14.

Sample Input 2

314 159 2653 589

Sample Output 2

602215194

Solution in C++14 (GCC 5.4.1) (judge verdict: Accepted)

/**
 *     author: qodjf
 *     created: 04.22.2020 00:11:45
 */
#include <bits/stdc++.h>
using namespace std;

using ll = long long;
const ll MOD = 1e9 + 7;

ll mul(ll a, ll b) { return a * b % MOD; }

ll add(ll a, ll b) { return (a + b) % MOD; }

ll sub(ll a, ll b) { return (a - b + MOD) % MOD; }

ll my_pow(ll a, ll b) {
  ll r = 1;
  while (b) {
    if (b & 1) r = mul(r, a);
    a = mul(a, a);
    b >>= 1;
  }
  return r;
}

ll my_inv(ll a) { return my_pow(a, MOD - 2); }

namespace Comb {
const int MAXK = 2e6 + 5;
int fac[MAXK], inv_fac[MAXK];

void init() {
  fac[0] = inv_fac[0] = 1;
  for (int i = 1; i < MAXK; ++i) {
    fac[i] = mul(fac[i - 1], i);
    inv_fac[i] = my_inv(fac[i]);
  }
}

int C(int a, int b) {
  return mul(fac[a], mul(inv_fac[b], inv_fac[a - b]));
}

}  // namespace Comb

int main() {
  ios::sync_with_stdio(false);
  cin.tie(nullptr);

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

  Comb::init();
  ll ans = 0;
  ll prev = 0;
  int lr = r1, lc = c1, rr = r1, rc = c1;
  for (int s = r1 + c1; s <= r2 + c2; s++) {
    ll cur = mul(prev, 2);
    if (lc == c1) {
      cur = add(cur, Comb::C(s - 1, lr));
    } else {
      cur = sub(cur, Comb::C(s - 1, lr));
    }
    if (rr == r1) {
      cur = add(cur, Comb::C(s - 1, rc));
    } else {
      cur = sub(cur, Comb::C(s - 1, rc));
    }

    if (lr < r2) {
      lr++;
    } else {
      lc++;
    }
    if (rc < c2) {
      rc++;
    } else {
      rr++;
    }

    ans = add(ans, cur);
    prev = cur;
  }
  cout << ans << endl;
}