#include<bits/stdc++.h>
using namespace std;
const int mod=1e9+7;
typedef long long ll;
int ksm(int x,int k)
{
	if(k==1) return x;
	ll ans=ksm(x,k/2);
	ans=ans*ans%mod;
	if(k%2) ans=ans*x%mod;
	return ans;
}
int cc(int x,int y)
{
	ll ans=1,div=1;
	int i;
	for(i=x;i>=x-y+1;i--) ans=ans*i%mod;
	
	for(i=y;i>=1;i--) div=div*i%mod;
	
	ans=ans*ksm(div,mod-2)%mod;
	return ans;
}
int main()
{
	int x,y;
	scanf("%d%d",&x,&y);
	int t=x+y;
	if(t%3){
		printf("0\n");
		return 0;
	}
	t/=3;
	if(t>x||t>y){
		printf("0\n");
		return 0;
	}
	printf("%d\n",cc(t,t*2-x));
	return 0;
}
### 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;
const int mod=1e9+7;
typedef long long ll;
int ksm(int x,int k)
{
	if(k==1) return x;
	ll ans=ksm(x,k/2);
	ans=ans*ans%mod;
	if(k%2) ans=ans*x%mod;
	return ans;
}
int cc(int x,int y)
{
	ll ans=1,div=1;
	int i;
	for(i=x;i>=x-y+1;i--) ans=ans*i%mod;
	
	for(i=y;i>=1;i--) div=div*i%mod;
	
	ans=ans*ksm(div,mod-2)%mod;
	return ans;
}
int main()
{
	int x,y;
	scanf("%d%d",&x,&y);
	int t=x+y;
	if(t%3){
		printf("0\n");
		return 0;
	}
	t/=3;
	if(t>x||t>y){
		printf("0\n");
		return 0;
	}
	printf("%d\n",cc(t,t*2-x));
	return 0;
}
```