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<vector>
#include<cstring>
using namespace std;
#define LL long long
#define MAXN 100000
#define MAXK 60
int n,len;LL L;
char s[MAXN+5];
int tr[MAXN+5][2],nd,pnt[MAXK+5];
int lowpos(LL x){
	int cnt=0;
    for(;!(x&1);cnt++,x>>=1);
    return cnt;
}
void Insert(){
	int p=0;
	for(int i=1;i<=len;i++){
		if(!tr[p][s[i]-'0'])tr[p][s[i]-'0']=++nd;
		p=tr[p][s[i]-'0'];
	}
}
void dfs(int x,int dep){
    for(int k=0;k<=1;k++)
	if(tr[x][k]==0) {if(L-dep>0)pnt[lowpos(L-dep)]^=1;}
	else dfs(tr[x][k],dep+1);
}
int main()
{
	scanf("%d%lld",&n,&L);
	for(int i=1;i<=n;i++){
		scanf("%s",s+1);
		len=strlen(s+1);
		Insert();
	}
	dfs(0,0);
	for(int i=0;i<=MAXK;i++)if(pnt[i]){printf("Alice\n");return 0;}
	printf("Bob\n");
}