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 <iostream>
#include <cstring>
using namespace std;
typedef long long LL;
const LL N = 1000000+10;
LL ch[N][2], tot;
LL n, L;
char s[N];
void insert(LL len, char * s) {
    LL now = 0; 
    for (LL i = 1; i <= len; i ++) {
        LL f = (s[i] == '1') ? 1 : 0;
        if (!ch[now][f]) {
            ch[now][f] = ++ tot;
        }
        now = ch[now][f];
    }
}
LL dfs(LL x, LL dep) {
    if (dep > L) return 0;
    if (x == 0 && dep != 0) {
        return (L-dep+1)&(-L+dep-1);
    }
    return dfs(ch[x][0], dep + 1) ^ dfs(ch[x][1], dep + 1);
}
int main() {
    scanf("%lld %lld", &n, &L);
    for (LL i = 1; i <= n; i ++) {
        scanf("%s", s+1);
        LL len = strlen(s+1);
        insert(len, s);
    }
    printf("%s\n", dfs(0, 0) ? "Alice" : "Bob");
}