#include<bits/stdc++.h>
using namespace std;
typedef long long ll;
const int maxn=1e9+7;
ll ksm(ll a,ll b)
{
	ll ans=1;
	while(b)
	{
		if(b&1) ans=ans*a%maxn;
		a=a*a%maxn;
		b>>=1;
	}
	return ans;
}
ll kl(ll a,ll b)
{
	ll ca=1,cb=1;
	if(a<b)
	{
		return 0;
	}
	else if(a==b)
	{
		return 1;
	}
	else
	{
		for(ll i=0;i<b;i++)
		{
			ca=ca*(a-i)%maxn;
			cb=cb*(b-i)%maxn;
		}
	}
	return ca*ksm(cb,maxn-2)%maxn;
}
int	main()
{
	
	ll x,y,m,n,k;
	scanf("%lld%lld",&x,&y);
	if((x+y)%3!=0)
	{
		printf("0\n");
	}
	else
	{
		m=(2*y-x)/3;
		n=(2*x-y)/3;
		if(m<0||n<0)
		{
			printf("0\n");
		}
		else printf("%lld\n",kl(m+n,m));
	}
	return 0;
 } 
### Prompt

Generate a CPP solution 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;
typedef long long ll;
const int maxn=1e9+7;
ll ksm(ll a,ll b)
{
	ll ans=1;
	while(b)
	{
		if(b&1) ans=ans*a%maxn;
		a=a*a%maxn;
		b>>=1;
	}
	return ans;
}
ll kl(ll a,ll b)
{
	ll ca=1,cb=1;
	if(a<b)
	{
		return 0;
	}
	else if(a==b)
	{
		return 1;
	}
	else
	{
		for(ll i=0;i<b;i++)
		{
			ca=ca*(a-i)%maxn;
			cb=cb*(b-i)%maxn;
		}
	}
	return ca*ksm(cb,maxn-2)%maxn;
}
int	main()
{
	
	ll x,y,m,n,k;
	scanf("%lld%lld",&x,&y);
	if((x+y)%3!=0)
	{
		printf("0\n");
	}
	else
	{
		m=(2*y-x)/3;
		n=(2*x-y)/3;
		if(m<0||n<0)
		{
			printf("0\n");
		}
		else printf("%lld\n",kl(m+n,m));
	}
	return 0;
 } 
```