Presidential Game

Two candidates are running in this year's presidential election, John Wee and Preston Wo. Taking a break from promoting their campaigns, they decide to play a game with an array $A$ of $N$ integers. The candidates make alternating moves until a single element remains, starting with John, the current president.

In each turn, John chooses a contiguous subarray of $A$ containing between $2$ and $K$ elements, inclusive, and replaces the subarray with a single element equal to the sum of all elements in the subarray. In each turn, Preston chooses a contiguous subarray of $A$ containing between $2$ and $K$ elements, inclusive, and replaces the subarray with a single element equal to the bitwise XOR of all elements in the subarray. The bitwise XOR of an array of integers $X$ is defined as follows, where $\oplus$ denotes the bitwise XOR operator.

$XOR(X) = \begin{cases} X_1 \oplus X_2 & \text{if }|X| = 2 \\ XOR([X_1, X_2, \dots, X_{|X|-1}]) \oplus X_{|X|} & \text{if }|X| > 2 \end{cases}$

Since John is candidate number 1, John wins the game if the single element left in the array is odd. Otherwise, if the single element left in the array is even, Preston wins the game. You want to predict who wins the game when both candidates play optimally.

The first line contains two integers $N$ $K$ ($2 \le K \le N \le 1000$), the length of the array and the maximum length of the subarray that can be chosen in each turn. The next line contains $N$ integers $A_i$ ($0 \le A_i \le 1000$), the array $A$.

Output in a single line the name of the winner, either John or Preston.