Codeforces 455B. A Lot of Games（字典树上博弈）

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).

Examples
input

output

input

output

input

output

4
0 0
1 0
0 1
1 1

1

BZOJ 2850: 巧克力王国（K-Dtree维护矩形中的点和）

3 3
1 2 5
3 1 4
2 2 1
2 1 6
1 3 5
1 3 7

5
0
4

HINT

1 <= n, m <= 50000，1 <= 10^9，-10^9 <= a, b, x, y <= 10^9。