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 int long long
#define mod 1000000007

const int MAX = 3000005;
int fac[MAX], inv[MAX], finv[MAX];

void pre(){
  inv[1]=1;
  for (int i = 2; i <MAX ; i++)
  {
    inv[i]=inv[mod%i]*(mod-mod/i)%mod;
  }
  fac[0]=finv[0]=1;
  for (int i = 1; i < MAX; ++i)
  {
    fac[i]=fac[i-1]*i%mod;
    finv[i]=finv[i-1]*inv[i]%mod;
  }
}
int ncr(int n, int r){
  if(r<0||r>n)return 0;
  return fac[n]*finv[r]%mod*finv[n-r]%mod;
}

signed main(){
    pre();
    
    int r1, c1, r2, c2;
    cin >> r1 >> c1 >> r2 >> c2;

    int ans = 0;

    for(int i = r1; i<=r2;i++){
        int cur = (c2+1)*ncr(i+c2+1, c2+1)%mod - (c1)*ncr(c1+i,c1)%mod;
        cur = (cur+mod)%mod;
        cur = cur*inv[i+1]%mod;
        ans = (ans+cur)%mod;
    }

    cout << ans << endl;


    return 0;
}
