MKTHNUM  Kth Number
English  Vietnamese 
You are working for Macrohard company in data structures department. After failing your previous task about key insertion you were asked to write a new data structure that would be able to return quickly kth order statistics in the array segment.
That is, given an array a[1 ... n] of different integer numbers, your program must answer a series of questions Q(i, j, k) in the form: "What would be the kth number in a[i ... j] segment, if this segment was sorted?"
For example, consider the array a = (1, 5, 2, 6, 3, 7, 4). Let the question be Q(2, 5, 3). The segment a[2 ... 5] is (5, 2, 6, 3). If we sort this segment, we get (2, 3, 5, 6), the third number is 5, and therefore the answer to the question is 5.
Input
The first line of the input contains n — the size of the array, and m — the number of questions to answer (1 ≤ n ≤ 100000, 1 ≤ m ≤ 5000).
The second line contains n different integer numbers not exceeding 10^9 by their absolute values — the array for which the answers should be given.
The following m lines contain question descriptions, each description consists of three numbers: i, j, and k (1 ≤ i ≤ j ≤ n, 1 ≤ k ≤ j  i + 1) and represents the question Q(i, j, k).
SAMPLE INPUT 7 3 1 5 2 6 3 7 4 2 5 3 4 4 1 1 7 3
Output
For each question output the answer to it — the kth number in sorted a[i ... j] segment. SAMPLE OUTPUT 5 6 3Note : naive solution will not work!!!
hide comments
free__bird:
20170612 08:35:20
took me 2 days to learn the concept of persistent tree,finally AC :) in one go.


barishnamazov:
20170611 13:44:39
why O((n + m)log^2(n)) doesn't get tle? 

mridul1809:
20170608 22:44:19
persistent segment tree...amazing DS :D 

sfialok98:
20170606 21:16:24
Finally Accepted,Learned Persistent Segment Trees....!!!!


joseluisacv2:
20170606 03:01:15
The number of queries is wrong. It is M<= 1e5


leafbebop:
20170531 05:16:35
Note: sometimes it is not the algorithms blocks you from AC, but the I/O speed.


mddaud001:
20170520 21:26:13
Trying to solve from last week


rihaz_zahir:
20170215 20:12:33
why array compression with sqrt decomposition + segment tree is giving tle?


crazymax:
20161031 15:01:26
Mo+ordered_set_tree (complexity with  Q*sqrt(N)*log(N)+N*sqrt(N)) solution gives TLE. :( 

Ravi kumar:
20161025 15:57:06
Increase time limit for java. there is not even a single accepted solution.

Added by:  ~!(*(@*!@^& 
Date:  20090224 
Time limit:  1s 
Source limit:  50000B 
Memory limit:  1536MB 
Cluster:  Cube (Intel G860) 
Languages:  All except: ERL JSRHINO 
Resource:  Northeastern Europe 2004 Northern Subregion 