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>
using namespace std;

typedef long long LL;
typedef pair<int, int> II;

const int MAXN = (int) 1e5 + 10;
int n; LL l;
char S[MAXN];

int TSize;
int nxt[MAXN][2];

void Insert() {
    int p = 0, len = strlen(S + 1);
    for (int i = 1; i <= len; ++i) {
        int c = S[i] - '0';
        if (nxt[p][c] == 0) nxt[p][c] = ++TSize;
        p = nxt[p][c];
    }
}

LL DFS(int u, int h = 0) {
    if (nxt[u][0] == 0 && nxt[u][1] == 0) return 0;
    LL cur = 0;
    if (nxt[u][0] != 0 && nxt[u][1] != 0) cur = 0; else
    cur = (l - h) & (h - l);
    if (nxt[u][0] != 0) cur ^= DFS(nxt[u][0], h + 1);
    if (nxt[u][1] != 0) cur ^= DFS(nxt[u][1], h + 1);
    return cur;
}

int main() {
    scanf("%d%lld", &n, &l);
    for (int i = 1; i <= n; ++i) {
        scanf("%s", S + 1);
        Insert();
    }

    puts(DFS(0) ? "Alice" : "Bob");
    return 0;
}