#include<bits/stdc++.h>
using namespace std;
typedef long long ll;
const int maxn=1e3+7;
int n;const int mod=1e9+7;
ll quickmod(ll x,ll y)
{
	ll ans=1;
	while(y)
	{
		if(y&1)
		{
			ans*=x;ans%=mod;
		}
		x*=x;x%=mod;y>>=1;
	}
	return ans;
}
int main()
{
	ll x,y;cin>>x>>y;
	if((x+y)%3!=0)
	{
		cout<<0<<endl;
		return 0;
	}
	else
	{
		ll tmp=(x+y)/3;
		ll num=y-tmp;
		if(num<0||num>tmp)
		{
			cout<<0<<endl;
			return 0;
		}
		//cout<<num<<" "<<tmp<<endl;
		ll ans=1;
		for(int i=tmp;i>=tmp-num+1;i--)
		{
			ans*=i;ans%=mod;
		}
		for(int i=num;i>=1;i--)
		{
			ans*=quickmod(i,mod-2);ans%=mod;
		}
		cout<<ans<<endl;
	}
 } 
### Prompt

Please provide a cpp coded solution to the problem described below:

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=1e3+7;
int n;const int mod=1e9+7;
ll quickmod(ll x,ll y)
{
	ll ans=1;
	while(y)
	{
		if(y&1)
		{
			ans*=x;ans%=mod;
		}
		x*=x;x%=mod;y>>=1;
	}
	return ans;
}
int main()
{
	ll x,y;cin>>x>>y;
	if((x+y)%3!=0)
	{
		cout<<0<<endl;
		return 0;
	}
	else
	{
		ll tmp=(x+y)/3;
		ll num=y-tmp;
		if(num<0||num>tmp)
		{
			cout<<0<<endl;
			return 0;
		}
		//cout<<num<<" "<<tmp<<endl;
		ll ans=1;
		for(int i=tmp;i>=tmp-num+1;i--)
		{
			ans*=i;ans%=mod;
		}
		for(int i=num;i>=1;i--)
		{
			ans*=quickmod(i,mod-2);ans%=mod;
		}
		cout<<ans<<endl;
	}
 } 
```