You are given a stream of ~n~ integers and an integer ~k~.

After each new integer arrives, report the ~k~-th smallest value among all numbers seen so far. If fewer than ~k~ numbers have been seen, print -1 for that step.

Input

The first line contains two integers ~n~ and ~k~.

The second line contains ~n~ integers ~a_1, a_2, \dots, a_n~, where ~a_i~ is the ~i~-th value in the stream.

Output

Print ~n~ lines. On line ~i~, print:

• the ~k~-th smallest value among ~a_1, a_2, \dots, a_i~, or
• -1 if ~i < k~.

Constraints

• ~1 \le k \le n \le 2 \cdot 10^5~
• ~-10^9 \le a_i \le 10^9~

Example 1

Input

8 3
5 2 7 1 9 3 4 6

Output

-1
-1
7
5
5
3
3
3

Explanation

After the first 3 values (5, 2, 7), the 3rd smallest is 7. After 6 values (5, 2, 7, 1, 9, 3), sorted order is 1, 2, 3, 5, 7, 9, so the 3rd smallest is 3.

Example 2

Input

5 1
10 -4 8 8 0

Output

10
-4
-4
-4
-4