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<cstring>
#include<cmath>
#include<algorithm>
#include<cstdlib>
#define ll long long
using namespace std;

const int N=100005;

int n,m,k,tot;
ll l,sg;
int ch[N][2];
char s[N];

ll lowbit(ll x){
	return x&-x;
}

void dfs(int k,int d){
	if (!ch[k][0]&&!ch[k][1]) return;
	if (ch[k][0]) dfs(ch[k][0],d+1);
	if (ch[k][1]) dfs(ch[k][1],d+1);
	if (!ch[k][0]||!ch[k][1]) sg^=lowbit(l-1ll*d);
}

int main(){
	int i,j;
	scanf("%d%lld",&n,&l);
	for (i=1;i<=n;i++){
		scanf("%s",s+1); m=strlen(s+1);
		k=0;
		for (j=1;j<=m;j++){
			if (!ch[k][s[j]-'0']) ch[k][s[j]-'0']=++tot;
			k=ch[k][s[j]-'0'];
		}
	}
	dfs(0,0);
	if (sg) printf("Alice\n");
	else printf("Bob\n");
	return 0;
}