#include <iostream>
#define N 1000005
using namespace std;
typedef long long ll;

ll n;
ll M=1e9+7, fac[N]={1,1}, inv[N]={1,1}, fiv[N]={1,1};

int main(void)
{
    int x,y;
    cin >> x >> y;
    int p=(2*x-y)/3;
    int q=(2*y-x)/3;
    if((x+y)%3!=0 || p<0 || q<0)
    {
        cout << 0;
        return 0;
    }
    for(int i=2; i<=N; i++) {
		fac[i] = fac[i-1] * i % M;
		inv[i] = inv[M%i] * (M-M/i) % M;
		fiv[i] = fiv[i-1] * inv[i] % M;
	}
	cout << fac[p+q]*fiv[p]%M*fiv[q]%M;
    return 0;
}

### Prompt

Develop a solution in Cpp 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 <iostream>
#define N 1000005
using namespace std;
typedef long long ll;

ll n;
ll M=1e9+7, fac[N]={1,1}, inv[N]={1,1}, fiv[N]={1,1};

int main(void)
{
    int x,y;
    cin >> x >> y;
    int p=(2*x-y)/3;
    int q=(2*y-x)/3;
    if((x+y)%3!=0 || p<0 || q<0)
    {
        cout << 0;
        return 0;
    }
    for(int i=2; i<=N; i++) {
		fac[i] = fac[i-1] * i % M;
		inv[i] = inv[M%i] * (M-M/i) % M;
		fiv[i] = fiv[i-1] * inv[i] % M;
	}
	cout << fac[p+q]*fiv[p]%M*fiv[q]%M;
    return 0;
}

```