#include<bits/stdc++.h>
#define MOD 1000000007
using namespace std;

long long modpow(long long a,long long n)
{
  long long res=1;
  while(n>0)
  {
    if(n&1)res=res*a%MOD;
    a=a*a%MOD;
    n>>=1;
  }
  return res;
}

int main()
{
long long X,Y,r,n;scanf("%lld %lld",&X,&Y);long long ans=1;
if((X+Y)%3!=0||max(X,Y)>min(X,Y)*2){printf("0\n");return 0;}
r=(2*X-Y)/3;n=X-r;
for(long long i=n;i>n-r;i--)ans=ans*i%MOD;
for(long long i=r;i>0;i--)
{
  ans=ans*modpow(i,MOD-2)%MOD;
}
printf("%lld\n",ans);
}

### 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<bits/stdc++.h>
#define MOD 1000000007
using namespace std;

long long modpow(long long a,long long n)
{
  long long res=1;
  while(n>0)
  {
    if(n&1)res=res*a%MOD;
    a=a*a%MOD;
    n>>=1;
  }
  return res;
}

int main()
{
long long X,Y,r,n;scanf("%lld %lld",&X,&Y);long long ans=1;
if((X+Y)%3!=0||max(X,Y)>min(X,Y)*2){printf("0\n");return 0;}
r=(2*X-Y)/3;n=X-r;
for(long long i=n;i>n-r;i--)ans=ans*i%MOD;
for(long long i=r;i>0;i--)
{
  ans=ans*modpow(i,MOD-2)%MOD;
}
printf("%lld\n",ans);
}

```