#include<bits/stdc++.h> 
#define ll long long
#define pb push_back
using namespace std;
ll a[500005],M=1000000007;
ll power(ll x,ll y)
{
	ll res=1;
	while(y)
	{
		if(y%2==1) res=(res*x)%M;
		x=(x*x)%M;
		y/=2;	
	}
	return res;
}
ll C(ll n,ll k)  
{  
    ll res=1;    
    if(k>n-k) k=n-k;  
    for(ll i = 0;i<k;i++)  
    {  
        res=(res*(n-i))%M;  
        res=(res*power(i+1,M-2))%M;  
    }  
    return res;  
}  
int main() 
{ 
	ll x,y;
	cin>>x>>y;
	if((x+y)%3==0)
	{
		if(x>=(x+y)/3&&x<=2*((x+y)/3)) cout<<C((x+y)/3,2*((x+y)/3)-x);
		else cout<<"0";
	}
	else cout<<"0";
	return 0; 
} 
### 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> 
#define ll long long
#define pb push_back
using namespace std;
ll a[500005],M=1000000007;
ll power(ll x,ll y)
{
	ll res=1;
	while(y)
	{
		if(y%2==1) res=(res*x)%M;
		x=(x*x)%M;
		y/=2;	
	}
	return res;
}
ll C(ll n,ll k)  
{  
    ll res=1;    
    if(k>n-k) k=n-k;  
    for(ll i = 0;i<k;i++)  
    {  
        res=(res*(n-i))%M;  
        res=(res*power(i+1,M-2))%M;  
    }  
    return res;  
}  
int main() 
{ 
	ll x,y;
	cin>>x>>y;
	if((x+y)%3==0)
	{
		if(x>=(x+y)/3&&x<=2*((x+y)/3)) cout<<C((x+y)/3,2*((x+y)/3)-x);
		else cout<<"0";
	}
	else cout<<"0";
	return 0; 
} 
```