A9662 | 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.

The first line contains two integers, $n$ and $k$ ( $1<=n<=10^{5}$ ; $1<=k<=10^{9}$ ).

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 $10^{5}$ . Each string of the group consists only of lowercase English letters.

If the player who moves first wins, print "First", otherwise print "Second" (without the quotes).