CF 455B-- A Lot of Games

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

思路：構造字典樹，自底向上遞推一下。fuck[x][0]爲1表示踩在節點x上能讓自己輸。fuck[x][1]爲1表示踩在節點x上能讓自己贏

#include <iostream>
#include <cstdio>
#include <cstring>
#include <queue>
#include <set>
#include <map>
#include <string>
#include <algorithm>
#include <cmath>

using namespace std;
#define inf 0x3f3f3f3f
#define maxn 100080
#define LL long long int
char str[maxn];
struct Node
{
	int id,dep;
	bool operator < (const Node & a)const
	{
		return dep < a.dep;
	}
}node[maxn];
struct Trie
{
	int first[maxn],ch[maxn],nxt[maxn],fuck[maxn][2];
	int cnt;
	void init()
	{
		memset(fuck,0,sizeof(fuck));
		cnt = 1;
		first[0] = -1;
	}
	int idx(char c)
	{
		return c - 'a';
	}
	void insert(char * s)
	{
		int u = 0,j;
		int len = strlen(s);
		for(int i = 0;i < len;i++)
		{
			int id = idx(s[i]);
			bool flag = false;
			for(j = first[u];j != -1;j = nxt[j])
			{
				if(ch[j] == id)
				{
					flag = true;
					break;
				}
			}
			if(flag)	u = j;
			else 
			{
				node[cnt].id = cnt;
				node[cnt].dep = i+1;
				ch[cnt] = id;
				first[cnt] = -1;
				nxt[cnt] = first[u];
				first[u] = cnt++;
				u = cnt-1;
			}
		}
	}
	void gao()
	{
		sort(node+1,node+cnt);
		for(int i = cnt-1;i >= 1;i--)//能讓自己贏
		{
			bool flag = true;
			for(int j = first[node[i].id];j != -1;j = nxt[j])
			{
				if(fuck[j][1])
				{
					flag = false;
					break;
				}
			}
			fuck[node[i].id][1] = flag;
		}
		for(int i = cnt-1;i >= 1;i--)//踩了這一步能讓自己輸嗎
		{
			bool flag = true;
			for(int j = first[node[i].id];j != -1;j = nxt[j])
			{
				if(fuck[j][0])
				{
					flag = false;
					break;
				}
			}
			fuck[node[i].id][0] = flag;
			if(first[node[i].id] == -1)	fuck[node[i].id][0] = 0;
		}
		for(int i = first[0];i != -1;i = nxt[i])
		{
			if(fuck[i][0])	fuck[0][0] = 1;
			if(fuck[i][1])	fuck[0][1] = 1;
		}
	}
}trie;
int main()
{
	//freopen("in.txt","r",stdin);
	int n,k;
	while(scanf("%d%d",&n,&k)==2)
	{
		trie.init();
		for(int i = 1;i <= n;i++)
		{
			scanf("%s",str);
			trie.insert(str);
		}
		trie.gao();
		if(trie.fuck[0][0] && trie.fuck[0][1])	cout << "First" << endl;
		else if(trie.fuck[0][0])
		{
			cout << "Second" << endl;
		}
		else if(trie.fuck[0][1])
		{
			if(k&1)	cout << "First" << endl;
			else cout << "Second" << endl;
		}
		else cout << "Second" << endl;
	}
}