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;

const int MAXN = 200005;

int lc[MAXN], rc[MAXN], top = 0, root = 0;
int sg[MAXN];

int N;
long long L;
char str[MAXN];

void push(int &nd, const char *str)
{
	if (!nd) nd = ++top;
	if (*str == '\0') return; 
	push(*str == '0' ? lc[nd] : rc[nd], str+1);
}

long long cnt = 0;
inline long long lowbit(long long i)
{ return i&(-i); }

void dfs(int nd, long long dep)
{
	if (!nd) return;
	dfs(lc[nd], dep-1), dfs(rc[nd], dep-1);
	if ((!lc[nd] || !rc[nd]) && lc[nd]+rc[nd]) {
	        cnt ^= lowbit(dep);
	}
}

int main()
{
	scanf("%d%lld", &N, &L);
	for (int i = 1; i <= N; i++) {
		scanf("%s", str);
		push(root, str);
	}
	dfs(root, L);
	if (cnt != 0) cout << "Alice" << endl;
	else cout << "Bob" << endl;
	return 0;
}