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;
#define rep(i, a, b) for(int i=(a); i<(b); i++)
#define rrep(i, a, b) for(int i=(a); i>=(b); i--)
typedef long long ll;
const ll mod = 1000000007;

const int MAX = 2100000;
ll fac[MAX], finv[MAX], inv[MAX];

void cominit()
{
  fac[0] = fac[1] = 1;
  finv[0] = finv[1] = 1;
  inv[1] = 1;
  for (ll i=2; i<MAX; i++) {
    fac[i] = fac[i-1] * i % mod;
    inv[i] = mod - inv[mod%i] * (mod/i) % mod;
    finv[i] = finv[i-1] * inv[i] % mod;
  }
}

ll com(ll n, ll k)
{
  if (n<k) return 0;
  if (n<0 || k<0) return 0;
  return fac[n] * (finv[k] * finv[n-k] % mod) % mod;
}

int main()
{
  ll r1, c1, r2, c2;
  cin >> r1 >> c1 >> r2 >> c2;
  cominit();
  ll ans = 0;
  ans += com(r2+c2+2, c2+1);
  ans -= com(r1+c2+1, r1);
  ans -= com(r2+c1+1, r2+1);
  ans += com(r1+c1, r1);
  ans = (ans + mod) % mod;
  cout << ans << endl;

  return 0;
}
