False cards

You have a deck of $N$ cards. Card $i$ carries the claim "at least $a_i$ of the cards below this one are false".

Once the cards are stacked in a line, every claim can be checked against the stack. A card whose claim holds is true, and a card whose claim fails is false. Whether a card is true or false depends only on how many false cards lie below it.

Find an order that stacks all $N$ cards so that exactly $K$ of them are false. Such an order might not exist at all.

The first line contains the integers $N$ and $K$ ($1 \le N \le 5 \times 10^5$, $0 \le K \le N$).

Each of the next $N$ lines contains one integer $a_i$ ($0 \le a_i \le 5 \times 10^5$).

Several orders can satisfy the condition, so a single answer is fixed by the following rule.

Sort the $N$ numbers written on the cards in non-decreasing order. Place the $N-K$ smallest on top of the deck in that non-decreasing order, then place the remaining $K$ below them in non-increasing order. If this deck holds exactly $K$ false cards, print its $N$ numbers on one line separated by single spaces, from the top card to the bottom card. Otherwise print -1.

If any order at all leaves exactly $K$ false cards, this deck is one of them.

Decide the claims from the bottom of the deck upward. Take the deck holding 0, 1, 3, 3, 2 from top to bottom.

The bottom card reads 2 and has no false card below it, so its claim fails and the card is false. The card above it reads 3 and has only 1 false card below it, so it is false. The next card reads 3 and has 2 false cards below it, so it is false. The next card reads 1 and has 3 false cards below it, so it is true. The top card reads 0 and is true. This deck holds 3 false cards in total.