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 <cstdio>
#include <string>
using namespace std;
const int N=1e5+10;
int t[N][2],sz=1;
void add(string s)
{
    int i,cur=0;
    for (i=0;i<s.length();i++)
    {
        if (t[cur][s[i]-'0']==0)
            t[cur][s[i]-'0']=sz++;
        cur=t[cur][s[i]-'0'];
    }
}
long long ans=0,l;
void dfs(int x, int d)
{
    if (bool(t[x][0])!=bool(t[x][1]))
        ans^=(l-d)&(d-l);
    if (t[x][0])
        dfs(t[x][0],d+1);
    if (t[x][1])
        dfs(t[x][1],d+1);
}
int main()
{
    int n,i;
    string s;
    scanf("%d%lld",&n,&l);
    for (i=1;i<=n;i++)
    {
        cin>>s;
        add(s);
    }
    dfs(0,0);
    if (ans)
        printf("Alice\n");
    else
        printf("Bob\n");
    return 0;
}