#include<bits/stdc++.h>
using namespace std;
typedef long long LL;
const LL 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;
}

int main(){
	LL x,y;
	scanf("%lld %lld",&x,&y);
	if(y < x) swap(x,y); 
	if((2*y-x) % 3 == 0){
		LL a = (2 * y - x) / 3;
		LL b = (x - a) / 2;
		printf("%lld",C(a+b,a));
	}
	else printf("0\n");
	return 0;
}
### Prompt

Your challenge is to write 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;
typedef long long LL;
const LL 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;
}

int main(){
	LL x,y;
	scanf("%lld %lld",&x,&y);
	if(y < x) swap(x,y); 
	if((2*y-x) % 3 == 0){
		LL a = (2 * y - x) / 3;
		LL b = (x - a) / 2;
		printf("%lld",C(a+b,a));
	}
	else printf("0\n");
	return 0;
}
```