Problem:


Score : 700 points

Problem Statement

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.

Sample Input 1

2 2
00
01

Sample Output 1

Alice

If Alice adds 1, Bob will be unable to add a new string.

Sample Input 2

2 2
00
11

Sample Output 2

Bob

There are two strings that Alice can add on the first turn: 01 and 10.
In case she adds 01, if Bob add 10, she will be unable to add a new string.
Also, in case she adds 10, if Bob add 01, she will be unable to add a new string.

Sample Input 3

3 3
0
10
110

Sample Output 3

Alice

If Alice adds 111, Bob will be unable to add a new string.

Sample Input 4

2 1
0
1

Sample Output 4

Bob

Alice is unable to add a new string on the first turn.

Sample Input 5

1 2
11

Sample Output 5

Alice

Sample Input 6

2 3
101
11

Sample Output 6

Bob



Sample input:
2 2
00
01


Sample output:
Alice

Submission status: Runtime Error

Solution code:
def main():
    N,L = map(int,input().split())
    if N==1:
        print("Alice")
        exit()
    keys = []
    count = 0
    for i in range(N):
        s = input()
        #merge node:
        while len(s)>0:
            if s[-1]=='1' and s[:-1]+'0' in keys:
                keys.remove(s[:-1]+'0')
                s = s[:-1]
            elif s[-1]=='0' and s[:-1]+'1' in keys:
                keys.remove(s[:-1]+'1')
                s = s[:-1]
            else:
                if s!="":
                    keys.append(s)
                break
    if len(keys)!=0:
        keys = sorted(keys,key=len,reverse=True)
    while len(keys)!=0:
        print(keys)
        j = keys[0]
        keys.remove(j)
        if j[:-1]!="":
            keys.append(j[:-1])
        j = j[:-1]
        #merge node
        while len(j)>0:
            if j[-1]=='1' and j[:-1]+'0' in keys:
                keys.remove(j[:-1]+'0')
                keys.remove(j)
                j = j[:-1]
                if j!="":
                    keys.append(j)
            elif j[-1]=='0' and j[:-1]+'1' in keys:
                keys.remove(j[:-1]+'1')
                keys.remove(j)
                j = j[:-1]
                if j!="":
                    keys.append(j)
            else:
                break
        keys = sorted(keys,key=len,reverse=True)
        count+=1
    print("Bob" if count&1 ==0 else "Alice")


if __name__=="__main__":
    main()

Submission status: Runtime Error

Solution code:
class TrieNode:
    def __init__(self, char):
        self.char = char
        self.nextnode = dict()
        self.is_indict = False


class Trie:
    def __init__(self, charset):
        self.charset = charset
        self.root = TrieNode('')

    def add(self, a_str):
        node = self.root
        for i, char in enumerate(a_str):
            if char not in node.nextnode:
                node.nextnode[char] = TrieNode(char)
            node = node.nextnode[char]
            if i == len(a_str) - 1:
                node.is_indict = True

    def dfs(self, node, dep):
        ret, cnt = 0, 0
        for s in '01':
            if s not in node.nextnode:
                cnt += 1
            else:
                ret ^= self.dfs(node.nextnode[s], dep + 1)
        dep += 1
        if cnt % 2:
            power2 = 0
            while dep > 0 and dep % 2 == 0:
                power2 += 1
                dep //= 2
            ret ^= 2 ** power2
        return ret

    def debug_output(self, node, now):
        print(node.char, list(node.nextnode.items()), node.is_indict, now)
        if node.is_indict:
            print(now)
        for n in node.nextnode.values():
            self.debug_output(n, now + n.char)

N, L = map(int, input().split())
T = Trie('01')
for _ in range(N):
    T.add(input())
# T.debug_output(T.root, '')
print("Alice" if T.dfs(T.root, 0) else "Bob")