#include <bits/stdc++.h>
using namespace std;

const int M=1e9+7;
const int MAX=1e6;

long long kai[MAX],kair[MAX],rev[MAX];

void com_p(){
  kai[0]=kai[1]=1;
  kair[0]=kair[1]=1;
  rev[1]=1;
  for(int i=2;i<MAX;i++){
    kai[i]=kai[i-1]*i%M;
    rev[i]=M-rev[M%i]*(M/i)%M;
    kair[i]=kair[i-1]*rev[i]%M;
  }
}
long long ncr(int n,int r){
  if(n<0||r<0) return 0;
  if(n<r) return 0;
  return kai[n]*(kair[r]*kair[n-r]%M)%M;
}

int main(){
  int x,y;
  cin>>x>>y;
  com_p();
  long long sum=0;
  for(int i=0;i<=x;i++){
    if(3*i==2*y-x){
      sum+=ncr(y-i,i);
      sum%=M;
    }
  }
  cout<<sum<<endl;
}
### Prompt

Please create a solution in cpp to the following problem:

There is a knight - the chess piece - at the origin (0, 0) of a two-dimensional grid.

When the knight is at the square (i, j), it can be moved to either (i+1,j+2) or (i+2, j+1).

In how many ways can the knight reach the square (X, Y)?

Find the number of ways modulo 10^9 + 7.

Constraints

* 1 \leq X \leq 10^6
* 1 \leq Y \leq 10^6
* All values in input are integers.

Input

Input is given from Standard Input in the following format:


X Y


Output

Print the number of ways for the knight to reach (X, Y) from (0, 0), modulo 10^9 + 7.

Examples

Input

3 3


Output

2


Input

2 2


Output

0


Input

999999 999999


Output

151840682

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;

const int M=1e9+7;
const int MAX=1e6;

long long kai[MAX],kair[MAX],rev[MAX];

void com_p(){
  kai[0]=kai[1]=1;
  kair[0]=kair[1]=1;
  rev[1]=1;
  for(int i=2;i<MAX;i++){
    kai[i]=kai[i-1]*i%M;
    rev[i]=M-rev[M%i]*(M/i)%M;
    kair[i]=kair[i-1]*rev[i]%M;
  }
}
long long ncr(int n,int r){
  if(n<0||r<0) return 0;
  if(n<r) return 0;
  return kai[n]*(kair[r]*kair[n-r]%M)%M;
}

int main(){
  int x,y;
  cin>>x>>y;
  com_p();
  long long sum=0;
  for(int i=0;i<=x;i++){
    if(3*i==2*y-x){
      sum+=ncr(y-i,i);
      sum%=M;
    }
  }
  cout<<sum<<endl;
}
```