Codeforces 455B

B. A Lot of Games

time limit per test
1 second

memory limit per test
256 megabytes

input
standard input

output
standard output

Andrew, Fedor and Alex are inventive guys. Now they invent the game with strings for two players.

Given a group of n non-empty strings. During the game two players build the word together, initially the word is empty. The players move in turns. On his step player must add a single letter in the end of the word, the resulting word must be prefix of at least one string from the group. A player loses if he cannot move.

Andrew and Alex decided to play this game k times. The player who is the loser of the i-th game makes the first move in the (i + 1)-th game. Guys decided that the winner of all games is the player who wins the last (k-th) game. Andrew and Alex already started the game. Fedor wants to know who wins the game if both players will play optimally. Help him.

Input

The first line contains two integers, n and k (1 ≤ n ≤ 105; 1 ≤ k ≤ 109).

Each of the next n lines contains a single non-empty string from the given group. The total length of all strings from the group doesn't exceed 105. Each string of the group consists only of lowercase English letters.

Output

If the player who moves first wins, print "First", otherwise print "Second" (without the quotes).
Sample test(s)
input
2 3
a
b
output
First
input
3 1
a
b
c
output
First
input
1 2
ab
output
Second

Trie树存储字符串，我们需要保存到达某个结点时是否必胜或者是否存在必败态。
win[u]表示在结点u是否必胜， lose[u]表示在结点u是否存在必败态。
Accepted Code:

 1 /*************************************************************************
 2     > File Name: D.cpp
 3     > Author: Stomach_ache
 4     > Mail: sudaweitong@gmail.com
 5     > Created Time: 2014年08月13日 星期三 14时10分37秒
 6     > Propose: 
 7  ************************************************************************/
 8 
 9 #include <cmath>
10 #include <string>
11 #include <cstdio>
12 #include <fstream>
13 #include <cstring>
14 #include <iostream>
15 #include <algorithm>
16 using namespace std;
17 /*Let's fight!!!*/
18 
19 const int maxn = 100005;
20 int ch[maxn][30];
21 
22 struct Trie {
23     int sz;
24     Trie() {
25           memset(ch[0], 0, sizeof(ch[0]));
26         sz = 1;
27     }
28     void insert(char *s);
29     void dfs(int u);
30 };
31 
32 inline void Trie::insert(char *s) {
33       int u = 0, n = (int)strlen(s);
34     for (int i = 0; i < n; i++) {
35           int id = s[i] - 'a';
36         if (!ch[u][id]) {
37               memset(ch[sz], 0, sizeof(ch[sz]));
38               ch[u][id] = sz++;
39         }
40         u = ch[u][id];
41     }
42 }
43 
44 bool win[maxn], lose[maxn];
45 inline void Trie::dfs(int u) {
46       bool flag = false;
47       for (int i = 0; i < 30; i++) if (ch[u][i]) {
48           flag = true;
49           int v = ch[u][i];
50           dfs(v);
51         if (!win[v]) win[u] = true;
52         if (!lose[v]) lose[u] = true; 
53     }
54     if (!flag) lose[u] = true;
55 }
56 
57 char str[maxn];
58 int main(void) {
59       int n, k;
60     Trie A;
61     scanf("%d %d", &n, &k);
62     while (n--) scanf("%s", str), A.insert(str);
63     memset(win, false, sizeof(win));
64     memset(lose, false, sizeof(lose));
65     A.dfs(0);
66     if ((win[0] && lose[0]) || (win[0] && k&1)) puts("First");
67     else puts("Second");
68 
69     return 0;
70 }