#include <stdio.h>
#define MOD (int)(1e9+7)
typedef long long ll;

int re(ll a){
  int m=MOD-2;
  ll res=1;
  while(m){
    if(m%2){
      res = res*a%MOD;
    }
    m /= 2;
    a = a*a%MOD;
  }
  return res;
}

int main(){
  int x,y;
  long long ans=1;
  
  scanf("%d%d",&x,&y);  
  if(x>y){int t=y;y=x;x=t;}
  if(2*x<y||(2*x-y)%3){printf("0\n");return 0;}
  
  int t = (2*x-y)/3;
  int sum = 2*t+(y-x);
  for(int i=0;i<t;i++){
    ans = ans*(sum-i)%MOD;
    ans = ans*re((ll)i+1)%MOD;
  }
  printf("%lld\n",ans);
  return 0;
}
### Prompt

Construct a cpp code solution to the problem outlined:

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 <stdio.h>
#define MOD (int)(1e9+7)
typedef long long ll;

int re(ll a){
  int m=MOD-2;
  ll res=1;
  while(m){
    if(m%2){
      res = res*a%MOD;
    }
    m /= 2;
    a = a*a%MOD;
  }
  return res;
}

int main(){
  int x,y;
  long long ans=1;
  
  scanf("%d%d",&x,&y);  
  if(x>y){int t=y;y=x;x=t;}
  if(2*x<y||(2*x-y)%3){printf("0\n");return 0;}
  
  int t = (2*x-y)/3;
  int sum = 2*t+(y-x);
  for(int i=0;i<t;i++){
    ans = ans*(sum-i)%MOD;
    ans = ans*re((ll)i+1)%MOD;
  }
  printf("%lld\n",ans);
  return 0;
}
```