#include <bits/stdc++.h>
using namespace std;
long long power(long long p,long long q,long long g){
  if(q==1)return p;
  else if(q%2==0){
    return (power(p,q/2,g)*power(p,q/2,g))%g;
  }
  else return (p*power(p,q-1,g))%g;
}
int main() {
  long long a,b;
  cin>>a>>b;
  long long big=1000000007;
  if((a+b)%3!=0)cout<<0<<endl;
  else {
    long long k=(a+b)/3;
    a-=k;
    b-=k;
    if(a<0||b<0)cout<<0<<endl;
    else {
      long long m=1,n=1;
      for(int i=k;i>k-a;i--){
        m*=i;
        m%=big;
      }
      for(int i=1;i<a+1;i++){
        n*=i;
        n%=big;
      }
      long long s=(m*power(n,big-2,big))%big;
        cout<<s<<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;
long long power(long long p,long long q,long long g){
  if(q==1)return p;
  else if(q%2==0){
    return (power(p,q/2,g)*power(p,q/2,g))%g;
  }
  else return (p*power(p,q-1,g))%g;
}
int main() {
  long long a,b;
  cin>>a>>b;
  long long big=1000000007;
  if((a+b)%3!=0)cout<<0<<endl;
  else {
    long long k=(a+b)/3;
    a-=k;
    b-=k;
    if(a<0||b<0)cout<<0<<endl;
    else {
      long long m=1,n=1;
      for(int i=k;i>k-a;i--){
        m*=i;
        m%=big;
      }
      for(int i=1;i<a+1;i++){
        n*=i;
        n%=big;
      }
      long long s=(m*power(n,big-2,big))%big;
        cout<<s<<endl;
    }
  }
}

```