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<cstdio>
#include<algorithm>
using namespace std;
int n, m, cnt;
long long L;
struct Trie {
	int ch[2], dep;
}T[301000];
char p[101000];
void Put(int a, char *key) {
	if (!(*key))return;
	int c = *key - '0';
	if (!T[a].ch[c]) {
		T[a].ch[c] = ++cnt;
		T[cnt].dep = T[a].dep + 1;
	}
	Put(T[a].ch[c], key + 1);
}
long long Get(long long a) {
	if (!a)return 0;
	if (a & 1)return 1;
	return Get(a >> 1) << 1;
}
int main() {
	int i, root = 1;
	scanf("%d%lld", &n, &L);
	cnt = 1;
	for (i = 0; i < n; i++) {
		scanf("%s", p);
		Put(root, p);
	}
	long long res = 0;
	for (i = 1; i <= cnt; i++) {
		if ((!T[i].ch[0]) != (!T[i].ch[1])) {
			res ^= Get(L - T[i].dep);
		}
	}
	if (res)puts("Alice");
	else puts("Bob");
}