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;

#define LL long long
#define N 300000
#define lowbit(x) ((x)&(-(x)))

LL n,m,x,ans,xb,cnt[N],son[N][2];
bool vis[N];
char s[N];

int main(){
    scanf("%lld%lld",&n,&m);
    vis[1]=1; son[1][0]=2; son[1][1]=3; xb=3;
    for (int i=1;i<=n;i++){
        scanf("%s",s+1); int l=strlen(s+1);
        x=1;
        for (int i=1;i<=l;i++){
            x=son[x][s[i]-'0'];
            if (!vis[x]){
                vis[x]=1; cnt[i-1]--;
                son[x][0]=++xb; son[x][1]=++xb;
                cnt[i]+=2;
            }
        }
    }
    for (int i=0;i<=m && i<=100000;i++) ans^=cnt[i]&1?lowbit(m-i):0;
    puts(ans?"Alice":"Bob");

    return 0;
}