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<stdio.h>
#include<vector>
#include<algorithm>
#include<string>
#include<iostream>
using namespace std;
typedef long long ll;
class segtree
{
public:
	int ko[1000000][2];
	int pt;
	ll ans;
	void init()
	{
		ko[0][0] = ko[0][1] = -1;
		pt = 1;
		ans = 0;
	}
	void add(string s)
	{
		int now = 0;
		for (int i = 0; i < s.size(); i++)
		{
			if (ko[now][s[i] - '0'] == -1)
			{
				ko[now][s[i] - '0'] = pt;
				ko[pt][0] = ko[pt][1] = -1;
				pt++;
			}
			now = ko[now][s[i] - '0'];
		}
	}
	void dfs(int node, ll len)
	{
		for (int i = 0; i < 2; i++)
		{
			if (ko[node][i] == -1)ans ^= len&-len;
			else dfs(ko[node][i], len - 1);
		}
	}
};
segtree tree;
int main()
{
	tree.init();
	int num;
	ll len;
	scanf("%d%lld", &num, &len);
	for (int i = 0; i < num; i++)
	{
		string s;
		cin >> s;
		tree.add(s);
	}
	tree.dfs(0, len);
	if (tree.ans == 0)printf("Bob\n");
	else printf("Alice\n");
}