#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
#define mod 1000000007

ll mode(ll a,ll b)
{
	if(b==0)return 1;
	ll ans=1;
	while(b>0)
	{
		if(b&1)ans=(ans*a)%mod;
		b=b>>1;
		a=((a%mod)*(a%mod))%mod;
	}return ans;
}
ll com(ll m,ll r)
{
	ll fmr=1,fr=1,fm=1,exp,ans;
	ll i;
	for(i=1;i<=m;i++)
	{
		fm=(fm*i)%mod;
		if(i==r)fr=fm;
		if(i==m-r)fmr=fm;
	}
	exp=(fmr*fr)%mod;
	exp=mode(exp,mod-2);
	ans=(fm*exp)%mod;
	return ans;
}

int main()
{
	ll x,y;
	cin>>x>>y;
	ll m,r;
	double m1,r1;
	m=(x+y)/3;r=(2*x-y)/3;
	m1=float(x+y)/3;r1=float(2*x-y)/3;
	if(r<0)cout<<0;
	else if(r>m)cout<<0;
	else if(m!=m1||r!=r1)cout<<0;
	else if(m==0)cout<<0;
	else if(r==0)cout<<1;
	else
	{
		cout<<com(m,r);
	}
	
}
### Prompt

Create a solution in cpp for 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;
#define mod 1000000007

ll mode(ll a,ll b)
{
	if(b==0)return 1;
	ll ans=1;
	while(b>0)
	{
		if(b&1)ans=(ans*a)%mod;
		b=b>>1;
		a=((a%mod)*(a%mod))%mod;
	}return ans;
}
ll com(ll m,ll r)
{
	ll fmr=1,fr=1,fm=1,exp,ans;
	ll i;
	for(i=1;i<=m;i++)
	{
		fm=(fm*i)%mod;
		if(i==r)fr=fm;
		if(i==m-r)fmr=fm;
	}
	exp=(fmr*fr)%mod;
	exp=mode(exp,mod-2);
	ans=(fm*exp)%mod;
	return ans;
}

int main()
{
	ll x,y;
	cin>>x>>y;
	ll m,r;
	double m1,r1;
	m=(x+y)/3;r=(2*x-y)/3;
	m1=float(x+y)/3;r1=float(2*x-y)/3;
	if(r<0)cout<<0;
	else if(r>m)cout<<0;
	else if(m!=m1||r!=r1)cout<<0;
	else if(m==0)cout<<0;
	else if(r==0)cout<<1;
	else
	{
		cout<<com(m,r);
	}
	
}
```