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 MAXN = 100010;
int nxt[MAXN][2], end[MAXN], dep[MAXN], idx = 1;
char buf[MAXN];
typedef long long LL;
LL get(LL x) { return x ? 1 << __builtin_ctzll(x) : 0; }
int main() {
	std::ios_base::sync_with_stdio(false), std::cin.tie(0);
	int n; LL L; std::cin >> n >> L;
	while (n --> 0) {
		std::cin >> buf; char * cur = buf;
		int now = 1;
		while (*cur) {
			int & nt = nxt[now][*cur++ - '0'];
			if (!nt) dep[nt = ++idx] = dep[now] + 1;
			now = nt;
		}
		end[now] = true;
	}
	LL ans = 0;
	for (int i = 1; i <= idx; ++i) if (!end[i])
		for (int j = 0; j != 2; ++j) if (!nxt[i][j])
			ans ^= get(L - dep[i]);
	std::cout << (ans ? "Alice" : "Bob") << std::endl;
	return 0;
}