#include<iostream>

using namespace::std;

#define MOD 1000000007

long long int fac[5000005],rev[5000005];

int main(){
	int x,y;
	cin>>x>>y;
	if((x+y)%3){
		cout<<0<<'\n';
		return 0;
	}
	int n=(x+y)/3;
	fac[0]=fac[1]=1;
	for(int i=2;i<=n;i++)
		fac[i]=(fac[i-1]*i)%MOD;
	rev[1]=1;
	for(int i=2;i<=n;i++)
		rev[i]=(MOD-(((MOD/i)%MOD)*rev[MOD%i])%MOD)%MOD;
	rev[0]=1;
	for(int i=2;i<=n;i++)
		rev[i]=(rev[i]*rev[i-1])%MOD;
	if(x<n || y<n)
		cout<<0<<'\n';
	else cout<<(fac[n]*((rev[y-n]*rev[x-n])%MOD))%MOD<<'\n';
}
### Prompt

Construct a cpp code solution to the problem outlined:

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<iostream>

using namespace::std;

#define MOD 1000000007

long long int fac[5000005],rev[5000005];

int main(){
	int x,y;
	cin>>x>>y;
	if((x+y)%3){
		cout<<0<<'\n';
		return 0;
	}
	int n=(x+y)/3;
	fac[0]=fac[1]=1;
	for(int i=2;i<=n;i++)
		fac[i]=(fac[i-1]*i)%MOD;
	rev[1]=1;
	for(int i=2;i<=n;i++)
		rev[i]=(MOD-(((MOD/i)%MOD)*rev[MOD%i])%MOD)%MOD;
	rev[0]=1;
	for(int i=2;i<=n;i++)
		rev[i]=(rev[i]*rev[i-1])%MOD;
	if(x<n || y<n)
		cout<<0<<'\n';
	else cout<<(fac[n]*((rev[y-n]*rev[x-n])%MOD))%MOD<<'\n';
}
```