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;

long long l,g;
string s[100005];

int binserch(int ok,int ng,int d)
{
	if (ng-ok<2)
	{
		return ok;
	}
	int mid=(ok+ng)/2;
	if (s[mid][d]=='0')
	{
		return binserch(mid,ng,d);
	}
	else
	{
		return binserch(ok,mid,d);
	}
}

void dfs(int x,int y,long long d)
{
	if (x==y)
	{
		long long z=l-d,now=2LL;
		while (z%now==0LL)
		{
			now*=2LL;
		}
		now/=2LL;
		g^=now;
		return;
	}
	else if (x+1==y&&s[x].size()==d+1)
	{
		return;
	}
	int z=binserch(x-1,y,d+1);
	dfs(x,z+1,d+1);
	dfs(z+1,y,d+1);
}

int main(int argc, char const *argv[])
{
	int n;
	cin>>n>>l;
	for (int i = 0; i < n; ++i)
	{
		cin>>s[i];
	}
	sort(s,s+n);
	int tmp=binserch(-1,n,0);
	g=0LL;
	dfs(0,tmp+1,0);
	dfs(tmp+1,n,0);
	if (g==0LL)
	{
		cout<<"Bob\n";
	}
	else
	{
		cout<<"Alice\n";
	}
	return 0;
}