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;

typedef long long lint;

#define rb(x) ((x)&(-(x)))

const int MAXN = 100010;
const lint MAXL = 1ll << 60;

int N;
lint L;
string S[MAXN];
lint ans;

void f(int s, int e, int i, string &str) {
	if(s > e) ans ^= rb(L - i + 1);
	else if(s < e || i < S[s].size()) {
		str.push_back('1');
		int l = lower_bound(S, S + N, str) - S;
		f(l, e, i + 1, str);
		str.pop_back();
		str.push_back('0');
		f(s, l - 1, i + 1, str);
		str.pop_back();
	}
}

int main() {
	ios::sync_with_stdio(0); cin.tie(0);
	cin >> N >> L;
	for(int i = 0; i < N; i++) cin >> S[i];

	sort(S, S + N);
	string str = "";
	f(0, N - 1, 0, str);
	cout << (ans ? "Alice" : "Bob") << "\n";
	return 0;
}