#include<bits/stdc++.h>
#define ll long long
using namespace std;
const ll mod=1e9+7;
ll x,y,a,b,fact[2000010];
ll power(ll a,ll b=mod-2)
{
	ll ans=1;
	while(b)
	{
		if(b&1)ans=ans*a%mod;
		a=a*a%mod;
		b>>=1;
	}
	return ans;
}
void init(ll n)
{
	fact[0]=1;
	for(ll i=1;i<=n;++i)
		fact[i]=fact[i-1]*i%mod;
}
ll C(ll n,ll m)
{
	return fact[n]*power(fact[m])%mod*power(fact[n-m])%mod;
}
int main()
{
	ios::sync_with_stdio(false);
	cin>>x>>y;
	b=(2*y-x)/3;
	a=(2*x-y)/3;
	init(a+b);
	if(2*a+b!=x||2*b+a!=y||a<0||b<0)
		cout<<0<<endl;
	else cout<<C(a+b,a)<<endl;
	return 0;
}
### 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>
#define ll long long
using namespace std;
const ll mod=1e9+7;
ll x,y,a,b,fact[2000010];
ll power(ll a,ll b=mod-2)
{
	ll ans=1;
	while(b)
	{
		if(b&1)ans=ans*a%mod;
		a=a*a%mod;
		b>>=1;
	}
	return ans;
}
void init(ll n)
{
	fact[0]=1;
	for(ll i=1;i<=n;++i)
		fact[i]=fact[i-1]*i%mod;
}
ll C(ll n,ll m)
{
	return fact[n]*power(fact[m])%mod*power(fact[n-m])%mod;
}
int main()
{
	ios::sync_with_stdio(false);
	cin>>x>>y;
	b=(2*y-x)/3;
	a=(2*x-y)/3;
	init(a+b);
	if(2*a+b!=x||2*b+a!=y||a<0||b<0)
		cout<<0<<endl;
	else cout<<C(a+b,a)<<endl;
	return 0;
}
```