Coin Game

Kevin and Nicky are playing a new game. The rules are as follows.

• The game starts with $n$ piles of coins, and pile $i$ holds $a_i$ coins.
• The two players take turns, and Kevin moves first.
• On a turn a player picks one nonempty pile and performs exactly one of these two moves.
  • Remove one coin from that pile.
  • This move is available only when the pile holds an even number of coins. Write that number as $2x$. Replace the pile with $k$ piles that hold $x$ coins each.

The player who takes the last coin wins. Given $n$, $k$, and the values $a_i$, print who wins when both players play optimally.

The first line contains $n$ and $k$. ($1 \le n \le 100000$, $1 \le k \le 10^9$)

The second line contains $n$ positive integers $a_1, a_2, \dots, a_n$ separated by spaces. ($1 \le a_i \le 10^9$)

Print the name of the winner, either Kevin or Nicky.