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>
using namespace std;

typedef long long ll;
const int maxn=100010<<2;
int n, val[maxn];
ll l;
char s[maxn];
int Max;
int e=1, ch[maxn][2];

ll calc(ll x){
	ll ret=1;
	while( !(x&1) && x>0 ) x>>=1, ret<<=1;
	return ret;
}
void insert(char *s){
	int o=1;
	for(int i=0;i<strlen(s);i++){
		int c=s[i]-'0';
		if(!ch[o][c]) ch[o][c]=++e;
		o=ch[o][c];
	}
	val[o]=1;
}

ll ans;
void dfs(int x,int dep){
	int cnt=(bool)ch[x][0]+(bool)ch[x][1];
	if(ch[x][0]) dfs(ch[x][0],dep+1); if(ch[x][1]) dfs(ch[x][1],dep+1);
	if(cnt==1){ ans^=calc(l-dep); return; }
}

int main(){

	scanf("%d%lld",&n,&l); l++;
	for(int i=1;i<=n;i++){
		scanf("%s",s); 
		insert(s);
	}
	dfs(1,1);
	printf("%s\n", ans?"Alice":"Bob");
	return 0;
}