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<algorithm>
#define MN 100005
using namespace std;
int n,s[MN][2],tt=1;char ch[MN];long long l;
long long dfs(int x,long long y){return (!y)?0:(!x?(y&(-y)):dfs(s[x][0],y-1)^dfs(s[x][1],y-1));}
int main(){
	scanf("%d%lld",&n,&l);
	for(int i=1;i<=n;i++){
		scanf("%s",ch);int len=strlen(ch),now=1;
		for(int j=0;j<len;j++){
			int tmp=ch[j]-'0';
			if(!s[now][tmp])s[now][tmp]=++tt;
			now=s[now][tmp];
		}
	}printf("%s\n",dfs(1,l+1)?"Alice":"Bob");
}