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
const int MOD=1e9+7;
int pw(int n,int k){
  assert(k>=0);
  int res=1;
  while(k){
    if(k&1)(res*=n)%=MOD;
    (n*=n)%=MOD;
    k>>=1;
  }
  return res;
}
int Factorial[5234567],Finverse[5234567];
inline void Cinit(){// limit is 5e6 /// write pw /// this takes 792ms at AtCoder
  Factorial[0]=1;
  for(int i=1;i<5e6;i++)Factorial[i]=(Factorial[i-1]*i)%MOD;
  for(int i=0;i<5e6;i++)Finverse[i]=pw(Factorial[i],MOD-2);
}
int nCk(int n,int k){
  if(n<k)return 0;if(k<0)return 0;
  if(!Factorial[0])Cinit();
  int res=Factorial[n];
  (res*=Finverse[k])%=MOD;
  (res*=Finverse[n-k])%=MOD;
  return res;
}
signed main(){
  int r1,c1,r2,c2;cin>>r1>>c1>>r2>>c2;
  cout<<((nCk(r2+c2+2,r2+1)-nCk(r1+c2+1,r1)-nCk(r2+c1+1,c1)+nCk(r1+c1,r1))%MOD+MOD)%MOD<<endl;
}
