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<algorithm>
#include<vector>
#include<queue>
#define lol(i,n) for(int i=0;i<n;i++)
#define mod 1000000007
typedef long long ll;
using namespace std;
#define N 200010
int t[N][2],len[N],ttop=0;
ll n,L,ans=0;
void Ins(int a){
	t[ttop][0]=0,t[ttop][1]=0;
	len[ttop]=a;
	ttop++;
}
ll g(ll k){
	int a=1;
	while(k%2==0)k/=2,a++;
	return a;
}
int main(){
	cin>>n>>L;
	Ins(0);
	lol(u,n){
		string s;cin>>s;
		int now=0;
		lol(i,s.size()){
			if(!t[now][s[i]-'0']){
				t[now][s[i]-'0']=ttop;
				Ins(i+1);
			}
			now=t[now][s[i]-'0'];
		}
	}
	lol(i,ttop){
		if(t[i][0]==0^t[i][1]==0){
			ans^=g(L-len[i]);
		}
	}
	cout<<(ans?"Alice":"Bob")<<endl;
	return 0;
}