Problem: For strings s and t, we will say that s and t are prefix-free when neither is a prefix of the other.

Let L be a positive integer. A set of strings S is a good string set when the following conditions hold true:

* Each string in S has a length between 1 and L (inclusive) and consists of the characters `0` and `1`.
* Any two distinct strings in S are prefix-free.



We have a good string set S = \\{ s_1, s_2, ..., s_N \\}. Alice and Bob will play a game against each other. They will alternately perform the following operation, starting from Alice:

* Add a new string to S. After addition, S must still be a good string set.



The first player who becomes unable to perform the operation loses the game. Determine the winner of the game when both players play optimally.

Constraints

* 1 \leq N \leq 10^5
* 1 \leq L \leq 10^{18}
* s_1, s_2, ..., s_N are all distinct.
* { s_1, s_2, ..., s_N } is a good string set.
* |s_1| + |s_2| + ... + |s_N| \leq 10^5

Input

Input is given from Standard Input in the following format:


N L
s_1
s_2
:
s_N


Output

If Alice will win, print `Alice`; if Bob will win, print `Bob`.

Examples

Input

2 2
00
01


Output

Alice


Input

2 2
00
11


Output

Bob


Input

3 3
0
10
110


Output

Alice


Input

2 1
0
1


Output

Bob


Input

1 2
11


Output

Alice


Input

2 3
101
11


Output

Bob

Solution (in CPP):

Solution:
#include <bits/stdc++.h>

#define ll long long

using namespace std;

const int N = (int)1e5 + 7;

int to[N][2];
int sz;

void add(string &t) {
  int v = 0;
  for (char c : t) {
    if (!to[v][c - '0']) {
      to[v][c - '0'] = ++sz;
    }
    v = to[v][c - '0'];
  }
}

int n;
ll l, sum;

ll get(ll x) {
  return x & -x;
}

void dfs(int v, int h = 0) {
  int cnt = (to[v][0] > 0) + (to[v][1] > 0);
  if (cnt == 1) {
    sum ^= get(l - h);
  }
  if (to[v][0])
    dfs(to[v][0], h + 1);
  if (to[v][1])
    dfs(to[v][1], h + 1);
}

int main() {
  scanf("%d %lld", &n, &l);
  string s;
  for (int i = 1; i <= n; i++) {
    cin >> s;
    add(s);
  }
  dfs(0);
  if (sum == 0) {
    cout << "Bob";
  } else {
    cout << "Alice";
  }
}