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;

int n, p;
ll l;
int lc[100100], rc[100100];
bool ed[100100];

char buf[100100];

void con(int cur, int i) {
    if (!buf[i]) {
        ed[cur] = 1;
        return;
    }
    int *xc = ((buf[i]=='0')?lc:rc);
    if (xc[cur]<0) {
        xc[cur]=p;
        lc[p]=rc[p]=-1;
        p++;
    }
    con(xc[cur],i+1);
}

ll c;
void dfs(int cur, ll d=0) {
    if (ed[cur]) return;
    if (~lc[cur]) dfs(lc[cur],d+1);
    else c^=(l-d)&(d-l);
    if (~rc[cur]) dfs(rc[cur],d+1);
    else c^=(l-d)&(d-l);
}

int main() {
    int i, j;

    scanf("%d%lld",&n,&l);
    lc[0]=rc[0]=-1;p=1;
    for (i=0;i<n;i++) {
        scanf("%s",buf);
        con(0,0);
    }
    dfs(0);
    puts(c?"Alice":"Bob");

    return 0;
}