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;
#define ran 111111
long long int q,sg;
char s[ran];
int L[ran],R[ran];
int Z;
long long int lowbit(long long int x){
	return x&-x;
}
void dfs(int x,int dep){
	if(L[x] == 0 && R[x] == 0)return;
	if(L[x] == 0){
		sg ^= lowbit(q-dep);
	}else
		dfs(L[x], dep+1);
	if(R[x] == 0){
		sg ^= lowbit(q-dep);
	}else
		dfs(R[x], dep+1);
}
int main(){
	int n;
	Z = 1;
	scanf("%d%lld",&n,&q);
	for(int i=0; i<n; i++){
		scanf("%s",s);
		int p = 1;
		for(int j=0; s[j]; j++){
			if(s[j] == '0'){
				if(L[p] == 0)L[p] = ++Z;
				p = L[p];
			}else{
				if(R[p] == 0)R[p] = ++Z;
				p = R[p];
			}
		}
	}
	sg=0;
	dfs(1,0);
	puts(sg?"Alice":"Bob");
	return 0;
}