Coin Game

Given n coin piles and a fixed k, players alternately remove a coin or split an even pile into k equal halves; decide the winner under optimal play.

Hard8Game theoryMathGreedyNo attempts yetTime limit2sMemory limit512 MB

Problem

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

  • The game starts with nn piles of coins, and pile ii holds aia_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 2x2x. Replace the pile with kk piles that hold xx coins each.

The player who takes the last coin wins. Given nn, kk, and the values aia_i, print who wins when both players play optimally.

Input

The first line contains nn and kk. (1n1000001 \le n \le 100000, 1k1091 \le k \le 10^9)

The second line contains nn positive integers a1,a2,,ana_1, a_2, \dots, a_n separated by spaces. (1ai1091 \le a_i \le 10^9)

Output

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