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 ll;

struct node{
	ll l, r, d;
	node() : l(0), r(0), d(0) {}
};

node T[202020];
char S[101010];
ll d, k, x;

void insert(ll p, char *S)
{
	if(!*S) return;
	
	if(*S == '0'){
		if(!T[p].l){
			T[p].l = ++k;
			T[k].d = T[p].d + 1;
		}
		insert(T[p].l, S + 1);
	}
	else{
		if(!T[p].r){
			T[p].r = ++k;
			T[k].d = T[p].d + 1;
		}
		insert(T[p].r, S + 1);
	}
}

int main()
{
	ll n, i;
	
	scanf("%lld%lld", &n, &d);
	
	k = 1;
	
	for(; n--; ){
		scanf("%s", S);
		insert(1, S);
	}
	
	for(i=1; i<=k; i++){
		if((T[i].l && !T[i].r) || (!T[i].l && T[i].r)){
			ll t = d - T[i].d;
			x ^= t & -t;
		}
	}
	
	printf("%s\n", x? "Alice" : "Bob");
	
	return 0;
}