#include<algorithm>
#include<iostream>
#include<cstdio>
#include<cstring>
#include<cmath>
using namespace std;
const long long MOD = 1e9 + 7;
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;
}
int main()
{
	int x,y,t;
	cin >> x >> y;
	long long m=(2*x-y)/3 + (2*y-x)/3;
	long long n=min((2*x-y)/3,(2*y-x)/3);
	if((2*x-y)%3!=0||(2*y-x)%3!=0){
		cout << 0 << endl;
	}
	else{
		cout << C(m,n) << endl;
	}
	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<algorithm>
#include<iostream>
#include<cstdio>
#include<cstring>
#include<cmath>
using namespace std;
const long long MOD = 1e9 + 7;
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;
}
int main()
{
	int x,y,t;
	cin >> x >> y;
	long long m=(2*x-y)/3 + (2*y-x)/3;
	long long n=min((2*x-y)/3,(2*y-x)/3);
	if((2*x-y)%3!=0||(2*y-x)%3!=0){
		cout << 0 << endl;
	}
	else{
		cout << C(m,n) << endl;
	}
	return 0;
}
```