#include <iostream>
using namespace std;

typedef long long ll;
const int MOD = 1000000007;

ll mod_pow(ll a, ll b) {
    if (b == 0) return 1;
    ll res = mod_pow(a * a % MOD, b / 2);
    if (b % 2 == 1) res = res * a % MOD;
    return res;
}

ll comb(ll a, ll b) {
    ll res = 1;
    for (int i = 0; i < b; i++) {
        res = res * (a - i) % MOD * mod_pow(i + 1, MOD - 2) % MOD;
    }
    return res;
}

int main() {
    ll X, Y;
    cin >> X >> Y;

    ll res = 0;
    for (ll n = 0; n < X + 1; n++) {
        if ((X - n) % 2 != 0) continue;
        if ((Y - 2 * n) != ((X - n) / 2)) continue;

        ll m = Y - 2 * n;
        res += comb(n + m, n);
    }

    cout << res % MOD << endl;
    return 0;
}
### Prompt

In CPP, your task is to solve the following problem:

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>
using namespace std;

typedef long long ll;
const int MOD = 1000000007;

ll mod_pow(ll a, ll b) {
    if (b == 0) return 1;
    ll res = mod_pow(a * a % MOD, b / 2);
    if (b % 2 == 1) res = res * a % MOD;
    return res;
}

ll comb(ll a, ll b) {
    ll res = 1;
    for (int i = 0; i < b; i++) {
        res = res * (a - i) % MOD * mod_pow(i + 1, MOD - 2) % MOD;
    }
    return res;
}

int main() {
    ll X, Y;
    cin >> X >> Y;

    ll res = 0;
    for (ll n = 0; n < X + 1; n++) {
        if ((X - n) % 2 != 0) continue;
        if ((Y - 2 * n) != ((X - n) / 2)) continue;

        ll m = Y - 2 * n;
        res += comb(n + m, n);
    }

    cout << res % MOD << endl;
    return 0;
}
```