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 rep(i, x, y) for (int i = x; i <= y; i++)
#define lowbit(x) ((x) & (-(x)))
using namespace std;

const int N = 1e5 + 10;
typedef long long ll;
ll n, L, ch[N][26], sz;
char s[N];

void insert(char s[]) {
    int u = 0, len = strlen(s + 1);
    rep(i, 1, len) {
        int c = s[i] - '0';
        if (!ch[u][c]) ch[u][c] = ++sz;
        u = ch[u][c];
    }
}

ll dfs(int x, int d) {
    if (!x && d) return lowbit(L - d + 1);
    return dfs(ch[x][0], d + 1) ^ dfs(ch[x][1], d + 1);
}

int main() {
    cin >> n >> L;
    rep(i, 1, n) {
        scanf("%s", s + 1);
        insert(s);
    }
    puts(dfs(0, 0) ? "Alice" : "Bob");
    return 0;
}