#include <bits/stdc++.h>
using namespace std;

typedef long long ll;
typedef long double ld;
typedef unsigned long long ull;

const ll mod = 1000000007;

ll inv(ll n){
	if(n == 1)return 1;
	return (mod - mod/n)*inv(mod%n)%mod;
}

int main(){
	ios::sync_with_stdio(false);
	cin.tie(NULL);
	cout.tie(NULL);
	cout<<setprecision(32);

	int x, y;
	cin>>x>>y;
	if((x + y)%3){
		cout<<0<<endl;
		exit(0);
	}
	int a = y - (x + y)/3;
	int b = x - (x + y)/3;
	if(a < 0 || b < 0){
		cout<<0<<endl;
		exit(0);
	}
	ll num = 1, den = 1;
	for(int i = 1; i <= b; i++){
		(num *= (a + i)) %= mod;
		(den *= i) %= mod;
	}
	ll ans = num*inv(den)%mod;
	cout<<ans<<endl;

	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;

typedef long long ll;
typedef long double ld;
typedef unsigned long long ull;

const ll mod = 1000000007;

ll inv(ll n){
	if(n == 1)return 1;
	return (mod - mod/n)*inv(mod%n)%mod;
}

int main(){
	ios::sync_with_stdio(false);
	cin.tie(NULL);
	cout.tie(NULL);
	cout<<setprecision(32);

	int x, y;
	cin>>x>>y;
	if((x + y)%3){
		cout<<0<<endl;
		exit(0);
	}
	int a = y - (x + y)/3;
	int b = x - (x + y)/3;
	if(a < 0 || b < 0){
		cout<<0<<endl;
		exit(0);
	}
	ll num = 1, den = 1;
	for(int i = 1; i <= b; i++){
		(num *= (a + i)) %= mod;
		(den *= i) %= mod;
	}
	ll ans = num*inv(den)%mod;
	cout<<ans<<endl;

	return 0;
}
```