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<map>
#include<cstdio>
#include<cstring>
#include<iostream>
#include<algorithm>
using namespace std;

typedef long long ll;
const int Maxn=1e5;

struct Trie {
	int son[2];
};
Trie t[Maxn+5];
int cnt=0;
void addstring(string tmp) {
	int rt=0;
	for(int i=0;i<(int)tmp.length();i++) {
		int ch=(int)tmp[i]-'0';
		if(!t[rt].son[ch])
			t[rt].son[ch]=++cnt;
		rt=t[rt].son[ch];
	}
}

int N;
ll L;
map<ll,int> g;
inline ll lowbit(ll x) {return x&(-x);}
void DFS(int rt,ll dep) {
	for(int i=0;i<2;i++) {
		if(t[rt].son[i]==0) {
			g[lowbit(L-dep+1)]^=1;
			continue;
		}
		DFS(t[rt].son[i],dep+1);
	}
}

int main() {
	#ifdef LOACL
	freopen("in.txt","r",stdin);
	freopen("out.txt","w",stdout);
	#endif
	scanf("%d %lld",&N,&L);
	for(int i=1;i<=N;i++) {
		string s;
		cin>>s;
		addstring(s);
	}
	DFS(0,1);
	for(map<ll,int>::iterator it=g.begin();it!=g.end();it++) {
		int t=it->second;
		if(t) {
			puts("Alice");
			return 0;
		}
	}
	puts("Bob");
	return 0;
}