#include <bits/stdc++.h>

using namespace std;

const long long M = 1e9+7;
long long f[1111111];

long long exp(long long a, long long e) {
    if(e == 1) return a;
    if(e%2) return (a*exp(a,e-1))%M;
    return exp((a*a)%M,e/2);
}

long long inv(long long a) { return exp(a,M-2); }

int main() {
    f[0] = 1;
    for(int i=1;i<1e6;i++) f[i] = (f[i-1]*i)%M;
    int a, b;
    cin >> a >> b;
    int a3 = 2*a-b, b3 = 2*b-a;
    if(a3%3 || b3%3 || a3 < 0 || b3 < 0) cout << 0 << endl;
    else {
        long long r = (f[(a3+b3)/3]*inv(f[a3/3]))%M;
        cout <<  (r*inv(f[b3/3]))%M<< endl;
    }
    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 <bits/stdc++.h>

using namespace std;

const long long M = 1e9+7;
long long f[1111111];

long long exp(long long a, long long e) {
    if(e == 1) return a;
    if(e%2) return (a*exp(a,e-1))%M;
    return exp((a*a)%M,e/2);
}

long long inv(long long a) { return exp(a,M-2); }

int main() {
    f[0] = 1;
    for(int i=1;i<1e6;i++) f[i] = (f[i-1]*i)%M;
    int a, b;
    cin >> a >> b;
    int a3 = 2*a-b, b3 = 2*b-a;
    if(a3%3 || b3%3 || a3 < 0 || b3 < 0) cout << 0 << endl;
    else {
        long long r = (f[(a3+b3)/3]*inv(f[a3/3]))%M;
        cout <<  (r*inv(f[b3/3]))%M<< endl;
    }
    return 0;
}

```