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D - Prefix K-th Max

Score : $400$ points

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.

3 2
1 2 3

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 $2$.

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

2
3
3
5
6
7
7