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 ll long long int
const int mod=1e9+7;
#define pb push_back
#define pii pair<ll,ll>
#define pi pair<int ,int> 
#define REP(i,a,n) for(int i=a;i<n;i++)
#define rep(i,a,n) for(int i=a;i>=n;i-- )
const int n=1e6;
ll inv[3*n];
ll fact[3*n];
ll infact[3*n];

ll nck(int n,int k){
  return fact[n]*infact[k]%mod*infact[n-k]%mod;
}

int main()
{    
   inv[1]=1;
   REP(i,2,3*n)
   {
       inv[i]=mod-mod/i*inv[mod%i]%mod;
   }
   fact[0]=1;infact[0]=1;
   REP(i,1,3*n)
   {
       fact[i]=((fact[i-1]%mod)*(i%mod))%mod;
       infact[i]=(infact[i-1]*inv[i])%mod;
   }
    
    ll r1,r2,c1,c2;
    cin>>r1>>c1>>r2>>c2;
    cout<<((nck(r2+c2+2,c2+1)-nck(r1+c2+1,c2+1)-nck(r2+c1+1,c1)+nck(r1+c1,c1)%mod+mod)%mod);
  
    return 0;
}