Problem Statement

Given are a permutation $P=(P_1,P_2,\\ldots,P_N)$ of $(1,2,\\ldots,N)$ and a positive integer $K$.

For each $i=K,K+1,\\ldots,N$, find the following.

• The $K$-th greatest value among the first $i$ terms of $P$.

Constraints

• $1 \\leq K \\leq N \\leq 5 \\times 10^5$
• $(P_1,P_2,\\ldots,P_N)$ is a permutation of $(1,2,\\ldots,N)$.
• All values in input are integers.

Input

Input is given from Standard Input in the following format:

$N$ $K$ $P_1$ $P_2$ $\\ldots$ $P_N$

Output

For each $i=K, K+1, \\ldots, N$, in this order, print the specified value in Problem Statement, separated by newlines.

Sample Input 1

3 2
1 2 3

Sample Output 1

1
2

• The $(K=)$ $2$-nd greatest value among the first $2$ terms of $P$, $(P_1,P_2)=(1,2)$, is $1$.
• The $(K=)$ $2$-nd greatest value among the first $3$ terms of $P$, $(P_1,P_2,P_3)=(1,2,3)$, is $2$.

Sample Input 2

11 5
3 7 2 5 11 6 1 9 8 10 4

Sample Output 2

2
3
3
5
6
7
7