K-th Smallest Stream

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

8 3
5 2 7 1 9 3 4 6

-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

5 1
10 -4 8 8 0

10
-4
-4
-4
-4