#include <bits/stdc++.h>
using namespace std;
typedef long long LL;
const int MOD=1e9+7;
int inv(int a)

{

	return a==1?1:(long long)(MOD-MOD/a)*inv(MOD%a)%MOD;

}

LL C(LL n,LL m)

{

	if(m<0)return 0;

	if(n<m)return 0;

	if(m>n-m)m=n-m;

	LL up=1,down=1;

	for(LL i=0;i<m;i++)

	{

		up=up*(n-i)%MOD;

		down=down*(i+1)%MOD;

	}

	return up*inv(down)%MOD;

}

//LL comb(LL m,LL n){
//	return (m==0 || n==0)?1:comb(m-1,n-1)*n/m;
//}
int main(){
	LL x,y;
	cin>>x>>y;
	if(x>y) swap(x,y);
	if((2*y-x)%3!=0){
		printf("%d\n",0);
	}
	else{
		LL a=(2*y-x)/3;
		LL b=(x-a)/2;
		printf("%lld\n",C(a+b,a));
	}
} 
### 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 <bits/stdc++.h>
using namespace std;
typedef long long LL;
const int MOD=1e9+7;
int inv(int a)

{

	return a==1?1:(long long)(MOD-MOD/a)*inv(MOD%a)%MOD;

}

LL C(LL n,LL m)

{

	if(m<0)return 0;

	if(n<m)return 0;

	if(m>n-m)m=n-m;

	LL up=1,down=1;

	for(LL i=0;i<m;i++)

	{

		up=up*(n-i)%MOD;

		down=down*(i+1)%MOD;

	}

	return up*inv(down)%MOD;

}

//LL comb(LL m,LL n){
//	return (m==0 || n==0)?1:comb(m-1,n-1)*n/m;
//}
int main(){
	LL x,y;
	cin>>x>>y;
	if(x>y) swap(x,y);
	if((2*y-x)%3!=0){
		printf("%d\n",0);
	}
	else{
		LL a=(2*y-x)/3;
		LL b=(x-a)/2;
		printf("%lld\n",C(a+b,a));
	}
} 
```