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>
#ifdef DEMETRIO
#define deb(...) fprintf(stderr,__VA_ARGS__)
#define deb1(x) cerr << #x << " = " << x << endl
#else
#define deb(...) 0
#define deb1(x) 0
#endif
#define pb push_back
#define mp make_pair
#define fst first
#define snd second
#define fore(i,a,b) for(int i=a,ThxDem=b;i<ThxDem;++i)
#define SZ(x) ((int)x.size())
using namespace std;
typedef long long ll;

int t[100005][2],nt=1;
char _s[100005];
int n;ll l,r;

void ins(string s){
	int k=0;
	for(char c:s){
		int d=c-'0';
		if(!t[k][d])t[k][d]=nt++;
		k=t[k][d];
	}
}

void dfs(int x, int d){
	if(!t[x][0]&&!t[x][1])return;
	if(!t[x][0]||!t[x][1]){
		ll a=l-d;
		if(a)r^=a&-a;
	}
	if(t[x][0])dfs(t[x][0],d+1);
	if(t[x][1])dfs(t[x][1],d+1);
}

int main(){
	scanf("%d%lld",&n,&l);
	while(n--){
		scanf("%s",_s);
		ins(string(_s));
	}
	dfs(0,0);
	puts(r?"Alice":"Bob");
	return 0;
}