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>
#define eb emplace_back
#define sz(V) ((int)(V).size())
#define allv(V) ((V).begin()),((V).end())
#define sorv(V) sort(allv(V))
#define rb(x) ((x)&(-(x)))
using namespace std;
typedef long long ll;

struct NOD {
	NOD() : l(NULL), r(NULL) {}
	NOD *l, *r;

	void make(char *S) {
		if('0' == S[0]) {
			if(NULL == l) l = new NOD();
			if(S[1]) l -> make(S+1);
		} else {
			if(NULL == r) r = new NOD();
			if(S[1]) r -> make(S+1);
		}
	}

	void get(vector<ll> &V, ll L) {
		if((NULL == l) != (NULL == r)) V.eb(L);
		if(NULL != l) l -> get(V, L-1);
		if(NULL != r) r -> get(V, L-1);
	}
} *rt;

ll L;
int N;

int main() {
	rt = new NOD();

	scanf("%d%lld", &N, &L);
	for(char str[100055]; N--;) {
		scanf(" %s", str);
		rt -> make(str);
	}

	vector<ll> V;
	rt -> get(V, L);

	ll ret = 0;
	for(ll v : V) {
		v = rb(v);
		ret ^= v;
	}

	puts(ret ? "Alice" : "Bob");
	return 0;
}