#include<bits/stdc++.h>
using namespace std;
long ncrmodp(long n,long r,long p){
  long ans = 1;
  long i;
  r = min(r,n-r);
  for(i=n;i>n-r;i--){
    ans *= i;
    ans %= p;
  }
  long tmp = 1;
  for(i=1;i<=r;i++){
    tmp *= i;
    tmp %= p;
  }
  for(long bit = 1;bit <= p-2;bit*=2){
    if(p-2 & bit){
      ans *= tmp;
      ans %= p;
    }
    tmp *= tmp;
    tmp%= p;
  }
  return ans;
}


int main(){
  long x,y;
  cin >> x >> y;
  if((x+y)%3 != 0 || x > y*2 || y > x*2)cout << 0 << endl;
  else{
    long const mod = 1000000007;
    int move = (x+y)/3;
    int xx = x - move;
    cout << ncrmodp(move,xx,mod)<<endl;

  }
}

### Prompt

Create a solution in Cpp for 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;
long ncrmodp(long n,long r,long p){
  long ans = 1;
  long i;
  r = min(r,n-r);
  for(i=n;i>n-r;i--){
    ans *= i;
    ans %= p;
  }
  long tmp = 1;
  for(i=1;i<=r;i++){
    tmp *= i;
    tmp %= p;
  }
  for(long bit = 1;bit <= p-2;bit*=2){
    if(p-2 & bit){
      ans *= tmp;
      ans %= p;
    }
    tmp *= tmp;
    tmp%= p;
  }
  return ans;
}


int main(){
  long x,y;
  cin >> x >> y;
  if((x+y)%3 != 0 || x > y*2 || y > x*2)cout << 0 << endl;
  else{
    long const mod = 1000000007;
    int move = (x+y)/3;
    int xx = x - move;
    cout << ncrmodp(move,xx,mod)<<endl;

  }
}

```