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<cstring>
#include<iostream>
#include<string>
#include<algorithm>
using namespace std;

#define ran 303333

int n;
long long l;
string s;

int nxt[ran][2], tail = 1;
long long ans;

long long sg(int dep) {
	long long rem = l-dep+1;
	return rem & -rem;
}

void dfs(int cur, int dep) {
	for(int i=0;i<2;i++)
		if (nxt[cur][i] == -1) ans ^= sg(dep);
		else dfs(nxt[cur][i], dep+1);
}

int main() {
	memset(nxt, -1, sizeof nxt);
	cin>>n>>l;
	for(int i=0;i<n;i++) {
		cin>>s;
		int it = 0;
		for(int j=0;j<s.size();j++) {
			int dir = s[j] - '0';
			if (nxt[it][dir]==-1) nxt[it][dir] = tail++;
			it = nxt[it][dir];
		}
	}
	ans = 0LL;
	dfs(0, 1);
	puts(ans==0 ? "Bob" : "Alice");
	
	return 0;
}