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<cstdio>
#include<cstring>
#include<cmath>
#include<cassert>
#include<iostream>
#include<iomanip>
#include<map>
#include<set>
#include<vector>
#include<algorithm>
#include<string>
#include<queue>
using namespace std;
#define DEBUG(x) cout<<#x<<"="<<x<<endl
#define DEBUG2(x,y) cout<<#x<<"="<<x<<","<<#y<<"="<<y<<endl
typedef long long ll;
// #define LOCAL
int idx;
const int MAXN=1e5+10;
int N;
ll L;
int ch[MAXN][2];
ll lowbit(ll x)
{
    return x&(-x);
}
void read()
{
    ios::sync_with_stdio(false);
    cin.tie(0);
    cin>>N>>L;
    for(int u=0;u<N;u++){
        string s;
        cin>>s;
        int flag=0;
        for(char c:s){
            int t=c-'0';
            if(ch[flag][t]==0)ch[flag][t]=++idx;
            flag=ch[flag][t];
        }
    }
}
ll glb=0;
void dfs(int rt,int d)
{
    if(ch[rt][0])dfs(ch[rt][0],d+1);
    else glb=glb^lowbit(L-d);
    if(ch[rt][1])dfs(ch[rt][1],d+1);
    else glb=glb^lowbit(L-d);
}
void solve()
{
    read();
    dfs(0,0);
    if(glb)cout<<"Alice";
    else cout<<"Bob";
}
int main()
{
#ifdef LOCAL
    freopen("in.txt","r",stdin);
#endif
    solve();
}