human
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

2 3
a
b

Output

First

Input

3 1
a
b
c

Output

First

Input

1 2
ab

Output

Second
class ... Write me a Python program to fix of at least one string from the group?
assistant
#Here is Python program to fix of at least one string from the group.
 TrieNode(object):

    def __init__(self, char: str):
        self.char = char
        self.children = []

        self.word_finished = False

        self.counter = 1

def add(root, word):

    node = root
    node.counter+=1
    for char in word:
        found_in_child = False

        for child in node.children:
            if child.char == char:

                child.counter += 1

                node = child
                found_in_child = True
                break

        if not found_in_child:
            new_node = TrieNode(char)
            node.children.append(new_node)

            node = new_node

    node.word_finished = True

def win(node):
    if node.children==[]:
        return False
    for child in node.children:
        if not win(child):
            return True

    return False

def loss(node):
    if node.children == []:
        return True
    for child in node.children:
        if not loss(child):
            return True

    return False



root=TrieNode("")
n,k=map(int,input().split())
for j in range(n):
    add(root,input())

win=win(root)
loss=loss(root)

if not win:
    print("Second")
else:
    if loss:
        print("First")
    else:
        if k%2:
            print("First")
        else:
            print("Second")