#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
const ll M = 1000000007;
ll n, m;
ll fact(ll n) {
	ll cnt = 1;
	for (int i=1; i<=n; i++) {
		cnt *= i;
		cnt %= M;
	}
	return cnt;
}

ll pow(ll a, ll n) {
	if (n==0)
		return 1;
	else {
		ll b = pow(a, n/2);
		if (n%2==0)
			return (b*b)%M;
		else return (b*((a*b)%M))%M;
	}
}

int main() {
	cin >> n >> m;
	if ((n+m)%3) 
		cout << 0;
	else {
		ll c = (n+m)/3;
		m -= c;
		n -= c;
		if(m<0 || n<0) 
			cout << 0;
		else {
			c = fact(c);
			m = fact(m);
			n = fact(n);
			cout << (c*((pow(n, M-2)*pow(m, M-2))%M))%M;
		}
	}
}
### 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;
typedef long long ll;
const ll M = 1000000007;
ll n, m;
ll fact(ll n) {
	ll cnt = 1;
	for (int i=1; i<=n; i++) {
		cnt *= i;
		cnt %= M;
	}
	return cnt;
}

ll pow(ll a, ll n) {
	if (n==0)
		return 1;
	else {
		ll b = pow(a, n/2);
		if (n%2==0)
			return (b*b)%M;
		else return (b*((a*b)%M))%M;
	}
}

int main() {
	cin >> n >> m;
	if ((n+m)%3) 
		cout << 0;
	else {
		ll c = (n+m)/3;
		m -= c;
		n -= c;
		if(m<0 || n<0) 
			cout << 0;
		else {
			c = fact(c);
			m = fact(m);
			n = fact(n);
			cout << (c*((pow(n, M-2)*pow(m, M-2))%M))%M;
		}
	}
}
```