#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
const int M = 1e9 + 7;

int x, y;

ll comb(int n, int m) {
    vector<ll> fact(2e6+1, 1);
    vector<ll> inv(2e6+1, 1);
    vector<ll> fi(2e6+1, 1);
    for (int i = 2; i <= 2e6; ++i) {
        fact[i] = (i * fact[i-1]) % M;
        inv[i] = M - (M/i) * inv[M%i] % M;
        fi[i] = (inv[i] * fi[i-1]) % M;
    }
    return (fact[n] * fi[m] % M) * fi[n-m] % M;
}

int main() {
    cin >> x >> y;
    if (((2*x-y)%3 != 0) || (2*x-y < 0) || ((x-(4*x-2*y)/3) < 0)) {
        cout << "0"; return 0;
    }
    int m = (2*x-y)/3;
    int n = x - 2*m;
    cout << comb(n+m, n);

    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;
const int M = 1e9 + 7;

int x, y;

ll comb(int n, int m) {
    vector<ll> fact(2e6+1, 1);
    vector<ll> inv(2e6+1, 1);
    vector<ll> fi(2e6+1, 1);
    for (int i = 2; i <= 2e6; ++i) {
        fact[i] = (i * fact[i-1]) % M;
        inv[i] = M - (M/i) * inv[M%i] % M;
        fi[i] = (inv[i] * fi[i-1]) % M;
    }
    return (fact[n] * fi[m] % M) * fi[n-m] % M;
}

int main() {
    cin >> x >> y;
    if (((2*x-y)%3 != 0) || (2*x-y < 0) || ((x-(4*x-2*y)/3) < 0)) {
        cout << "0"; return 0;
    }
    int m = (2*x-y)/3;
    int n = x - 2*m;
    cout << comb(n+m, n);

    return 0;
}

```