Amazon Web Services has n servers where the ith server's vulnerability score is vulnerability$[$i$].$ A client wants to deploy their application on a group of m contiguous servers. The vulnerability of a group is defined as the kth minimum vulnerability among the chosen servers. Find the vulnerability of each possible group of m contiguous servers the client can choose.

Example:

k $=2$

m $=3$

vulnerability $=[1,3,2,1]$

There are $2$ contiguous groups of m $=3$ servers: $[1,3,2]$ and $[3,2,1].$

The k $=2$nd lowest vulnerability in each group is $2.$

Return the answers for each group, in order: $[2,2].$

Function Description

Complete the function findKthMinimumVulnerability in the editor below.

findKthMinimumVulnerability has the following parameter$($s$)$:

int k: the order of the vulnerability to find

int m: the number of servers in a group

int vulnerability$[$n$]$: the vulnerabilities of each server

Returns:

int$[$n $-$ m $+1]$: the ith element represents the kth minimum vulnerability among the vulnerabilities of all the servers in the ith contiguous group.

Constraints

$1<=$ k $<=$ m $<=$ n $<=3*105$

$1<=$ vulnerability$[$i$]<=109$

Input Format For Custom Testing

The first line contains an integer, k$,$ the order of the vulnerability to find.

The second line contains an integer, m$,$ the number of servers in a group.

The third line contains an integer, n$,$ the size of vulnerability.

Each line i of the n subsequent lines $($where $0<=$ i $<$ n$)$ contains an integer, vulnerability$[$i$].$

Sample Case $0$

Sample Input For Custom Testing

STDIN FUNCTION

$-------------$

$3->$ order of vulnerability k $=3$

$4->$ servers in a group m $=4$

$5->$ number of servers n $=5$

$4->$ vulnerability $=[4,2,3,1,1]$

$2$

$3$

$1$

$1$

Sample Output

$3$

$2$

Explanation

The first group of servers is $[4,2,3,1]$ or $[1,2,3,4]$ when sorted. The $3$rd minimum vulnerability is $3.$

The second group of servers is $[2,3,1,1],$ or $[1,1,2,3]$ when sorted. The $3$rd minimum vulnerability is $2.$

Sample Case $0$

Sample Input For Custom Testing

STDIN FUNCTION

$-------------$

$3->$ order of vulnerability k $=3$

$4->$ servers in a group m $=4$

$5->$ number of servers n $=5$

$4->$ vulnerability $=[4,2,3,1,1]$

$2$

$3$

$1$

$1$

Sample Output

$3$

$2$

Explanation

The first group of servers is $[4,2,3,1]$ or $[1,2,3,4]$ when sorted. The $3$rd minimum vulnerability is $3.$

The second group of servers is $[2,3,1,1],$ or $[1,1,2,3]$ when sorted. The $3$rd minimum vulnerability is $2.$