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;
#define finish(x) return cout << x << endl, 0
#define ll long long

const int N = 100001;

int n, ch[N][2], en[N];
ll L, ans;
int cn;

void add(string &s){
    int node = 0;
    for(auto &i : s){
        int x = i - '0';
        if(ch[node][x] == -1){
            ch[node][x] = ++cn;
        }
        node = ch[node][x];
    }
    en[node] = 1;
}
void go(int node, ll dep){
    if(en[node]) return;
    if(ch[node][0] == -1) ans ^= dep ^ -dep;
    else go(ch[node][0], dep - 1);
    if(ch[node][1] == -1) ans ^= dep ^ -dep;
    else go(ch[node][1], dep - 1);
}
int main(){
    ios_base::sync_with_stdio(0);
    cin.tie(0);
    memset(ch, -1, sizeof ch);
    cin >> n >> L;
    for(int i = 0 ; i < n ; i++){
        string s;
        cin >> s;
        add(s);
    }
    go(0, L);
    if(ans) cout << "Alice\n";
    else cout << "Bob\n";
}