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>


const int N = 100005;

int nxt[N][2], idx, n, dep[N]; bool end[N];
long long l;
std::string s;

void insert(const std::string &s) {
	int p = 0;
	for (char ch : s) {
		int v = ch & 1;
		if (!nxt[p][v])
			nxt[p][v] = ++idx, dep[idx] = dep[p] + 1;
		p = nxt[p][v];
	}
	end[p] = 1;
}

long long lowbit(long long x) {return x & -x;}
long long calc(int d) {return lowbit(l - d + 1);}

int main() {
	std::ios::sync_with_stdio(0), std::cin.tie(0);
	std::cin >> n >> l;
	for (int i = 0; i < n; ++i)
		std::cin >> s, insert(s);
	long long ans = 0;
	for (int i = 0; i <= idx; ++i)
		if (!end[i] && (!nxt[i][0] ^ !nxt[i][1]))
			ans ^= calc(dep[i] + 1);
	std::cout << (ans ? "Alice" : "Bob") << '\n';
	return 0;
}