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 ai 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 ai, print who wins when both players play optimally.
Input
The first line contains n and k. (1≤n≤100000, 1≤k≤109)
The second line contains n positive integers a1,a2,…,an separated by spaces. (1≤ai≤109)
Output
Print the name of the winner, either Kevin or Nicky.