#include<bits/stdc++.h>
using namespace std;
const int mod=1000000007;
int inv(int a);
long long  C(long long n,long long m);
int main(){
	long long x,y;
	cin>>x>>y;
	long long a,b;
	a=2*x-y;
	b=2*y-x;
	if(a%3!=0||b%3!=0)
		cout<<0<<endl;
	else {
		a=a/3;b=b/3;
		cout<<C(a+b,a)%mod<<endl;
	}
	return 0;
} 



int inv(int a)
{
	return a==1?1:(long long)(mod-mod/a)*inv(mod%a)%mod;
}
long long C(long long n,long long m)
{
	if(m<0)return 0;
	if(n<m)return 0;
	if(m>n-m)m=n-m;
	long long up=1,down=1;
	for(long long i=0;i<m;i++)
	{
		up=up*(n-i)%mod;
		down=down*(i+1)%mod;
	}
	return up*inv(down)%mod;
}
### 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;
const int mod=1000000007;
int inv(int a);
long long  C(long long n,long long m);
int main(){
	long long x,y;
	cin>>x>>y;
	long long a,b;
	a=2*x-y;
	b=2*y-x;
	if(a%3!=0||b%3!=0)
		cout<<0<<endl;
	else {
		a=a/3;b=b/3;
		cout<<C(a+b,a)%mod<<endl;
	}
	return 0;
} 



int inv(int a)
{
	return a==1?1:(long long)(mod-mod/a)*inv(mod%a)%mod;
}
long long C(long long n,long long m)
{
	if(m<0)return 0;
	if(n<m)return 0;
	if(m>n-m)m=n-m;
	long long up=1,down=1;
	for(long long i=0;i<m;i++)
	{
		up=up*(n-i)%mod;
		down=down*(i+1)%mod;
	}
	return up*inv(down)%mod;
}
```