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,n) for(int i = 0; i < (int)n; i++)
using ll = long long;
const int MAX = 5e6;
const ll mod = 1e9+7;

ll fac[MAX], finv[MAX], inv[MAX];

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

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

ll f(ll x, ll y) {
  ll res = 0;
  rep(i,x+1) {
    (res += COM(y+i+1,i+1)) %= mod;
  }
  return res;
}

int main(){
  ll a, b, c, d;
  cin >> a >> b >> c >> d;
  COMinit();
  ll ans = f(c,d) - f(c,b-1) - f(a-1,d) + f(a-1,b-1);
  cout << ((ans % mod) + mod) % mod << endl;
  return 0;
}