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;

char c[111111];

int main()
{
	long long n, l;
	cin >> n >> l;
	vector<string> v;
	for (int i = 0; i < n; i++) {
		scanf("%s", c);
		v.push_back(c);
	}
	sort(v.begin(), v.end());
	v.push_back("a");
	fill(c, c + v.front().length(), 0);
	auto x = 0ll;
	for (auto it = v.begin() + 1;; ++it) {
		int r = 0;
		while (it[0][r] == it[-1][r])
			r++;
		if (*it == "a") r = -1;
		for (int i = r + 1; i < it[-1].length(); i++) {
			if (c[i]) continue;
			auto y = l - i;
			for (n = 1; y % 2 == 0; n *= 2)
				y /= 2;
			x ^= n;
		}
		if (r < 0) break;
		c[r] = 1;
		fill(c + r + 1, c + it->length(), 0);
	}
	cout << (x ? "Alice" : "Bob") << endl;
	return 0;
}