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>
#define int long long
using namespace std;
int n,l;
char s[100005];
int ch[100006][2];
int cnt,root;
void add()
{
	int len=strlen(s);int now=root;
	for(int j=0;j<len;j++)
	{
		int c=s[j]-'0';
		if(!ch[now][c])ch[now][c]=++cnt;
		now=ch[now][c];
	}
}
int ans;
void dfs(int x,int nw)
{
	if(ch[x][0])dfs(ch[x][0],nw+1);
	if(ch[x][1])dfs(ch[x][1],nw+1);
	if(!ch[x][0]&&!ch[x][1])return ;
	if(ch[x][0]&&ch[x][1])return ;
	int tmp=1,g=l-nw;
	while(g%2==0)
	{
		tmp<<=1;g>>=1;
	}
	ans^=tmp;
}
signed main()
{
	cin>>n>>l;root=++cnt;
	for(int i=1;i<=n;i++)
	{
		scanf("%s",s);
		add();
	}
	dfs(root,0);
	if(ans==0)puts("Bob");
	else puts("Alice");
	return 0;
}