// Author: HarshKumar

#include <bits/stdc++.h>
using namespace std;
#define ll int64_t
const ll N = 1e6 + 6, M = 1e9 + 7;
ll f[N] = {1};
ll in(ll a, ll b = M - 2)
{
    ll r = 1;
    while (b)
    {
        if (b % 2)
            r = (r * a) % M;
        a = (a * a) % M;
        b /= 2;
    }
    return r;
}
int main()
{
    ios::sync_with_stdio(false), cin.tie(nullptr);
    for (ll i = 1; i < N; i++)
        f[i] = (f[i - 1] * i) % M;
    ll x, y;
    cin >> x >> y;
    ll a = 2 * x - y;
    ll b = 2 * y - x;
    if (a < 0 || b < 0 || a % 3 || b % 3)
        return cout << 0, 0;
    a /= 3;
    b /= 3;
    cout << f[a + b] * in(f[a]) % M * in(f[b]) % M;
}
### 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
// Author: HarshKumar

#include <bits/stdc++.h>
using namespace std;
#define ll int64_t
const ll N = 1e6 + 6, M = 1e9 + 7;
ll f[N] = {1};
ll in(ll a, ll b = M - 2)
{
    ll r = 1;
    while (b)
    {
        if (b % 2)
            r = (r * a) % M;
        a = (a * a) % M;
        b /= 2;
    }
    return r;
}
int main()
{
    ios::sync_with_stdio(false), cin.tie(nullptr);
    for (ll i = 1; i < N; i++)
        f[i] = (f[i - 1] * i) % M;
    ll x, y;
    cin >> x >> y;
    ll a = 2 * x - y;
    ll b = 2 * y - x;
    if (a < 0 || b < 0 || a % 3 || b % 3)
        return cout << 0, 0;
    a /= 3;
    b /= 3;
    cout << f[a + b] * in(f[a]) % M * in(f[b]) % M;
}
```