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 For(i, j, k) for(int i = j; i <= k; i++)
#define Forr(i, j, k) for(int i = j; i >= k; i--)
#define pb push_back

using namespace std;

const int N = 100010;

typedef long long LL;

LL sg(LL x){
	++x;
	return x & (-x);
}

struct Trie{
	
	int ch[N][2], node;
	
	void insert(char* S, int l){
		int o = 0;
		For(i, 1, l){
			int &c = ch[o][S[i] - '0'];
			if(!c) c = ++node;
			o = c;
		}
	}

	LL calc(int o, LL dep){
		if(!ch[o][0] && !ch[o][1]) return 0;
		LL ret = 0;
		For(i, 0, 1) 
			if(!ch[o][i]) ret ^= sg(dep - 1);
			else ret ^= calc(ch[o][i], dep - 1);
		return ret;
	}

}T;

int n;
LL L;
char S[N];

int main(){
	
	scanf("%d%lld", &n, &L);
	For(i, 1, n){
		scanf("%s", S + 1);
		int l = strlen(S + 1);
		T.insert(S, l);
	}

	puts(!T.calc(0, L) ? "Bob" : "Alice");

	return 0;
}