LogiQuest

400. K-th Largest in a Stream

MediumHeap

Numbers arrive one by one. After each arrival print the k-th largest so far, or -1 if fewer than k numbers have arrived.

Input format

Line 1: n k Line 2: n integers

Output format

n answers.

Example 1

Input

6 3
4 5 8 2 3 10

Output

-1 -1 4 4 4 5

Example 2

Input

3 1
5 1 9

Output

5 5 9

Constraints

1 ≤ k ≤ n ≤ 10⁵

Read input from standard input and print the answer to standard output. Your code is judged against 3 test cases, most of them hidden.

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