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 <algorithm>
#include <iostream>
#include <cstring>
#include <cstdlib>
#include <utility>
#include <cstdio>
#include <vector>
#include <queue>
#include <stack>
#include <set>
#include <map>
#define mp make_pair
#define pb push_back
using namespace std; 
typedef long long ll; 
int son[100005][2]; 
char str[100005]; 
ll tot_dep, sg[100005]; 
inline int chk(ll x)
{
	int res = 0; 
	if (!x)
		return 0; 
	while (x & 1 ^ 1)
	{
		res++; 
		x >>= 1; 
	}
	return res; 
}
void dfs(int u, int dep = 0)
{
	if (!u)
		return; 
	int l = son[u][0], r = son[u][1]; 
	dfs(l, dep + 1); 
	dfs(r, dep + 1); 
	sg[0] = 1ll << chk(tot_dep - dep); 
	sg[u] = sg[l] ^ sg[r]; 
}
int main()
{
	// freopen("ARC087-E.in", "r", stdin); 
	int n, tot = 1; 
	scanf("%d%lld", &n, &tot_dep); 
	for (int i = 0; i < n; i++)
	{
		scanf("%s", str); 
		int u = 1, len = strlen(str); 
		for (int j = 0; j < len; j++)
		{
			if (!son[u][str[j] - '0'])
				son[u][str[j] - '0'] = ++tot; 
			u = son[u][str[j] - '0']; 
		}
	}
	dfs(1); 
	puts(sg[1] ? "Alice" : "Bob");
	return 0; 
}