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<algorithm>
#include<cstring>
#define ll long long
using namespace std;
ll n,m,cnt=1,ans,tot,bi[30],x[100010];
char ss[100010];
ll cal(ll k)
{
	ll s=1;
	while(!(k&1) && k)k/=2,s*=(ll)2; 
	return s;
}
struct tri
{
	int ch[1000010][2],v[1000010];
	void insert(int j)
	{
		int i,s,a,b,k;
		k=1;
		for(i=1;i<=j;i++)
		{
			b=x[i];
			if(!ch[k][b])ch[k][b]=++cnt;
			k=ch[k][b];
		}
		v[k]=1;
	}
	void ff(int k,int de)
	{
		if(v[k])return ;
		if(ch[k][0])ff(ch[k][0],de-1);
		else ans^=cal(de);
		if(ch[k][1])ff(ch[k][1],de-1);
		else ans^=cal(de);
	}
}tr;
int main()
{
	int i,s,a,b,j,k;
	scanf("%lld%lld",&n,&m);
	for(i=1;i<=n;i++)
	{
		scanf(" %s",ss);k=strlen(ss);
		for(s=1;s<=k;s++)x[s]=(ss[s-1]=='1');
		tr.insert(k);
	}
	tr.ff(1,m);
	if(ans)printf("Alice");
	else printf("Bob");
	return 0;
}