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
shiva_swag1:
20160624 21:10:51
binary search +persistence segment tree..


oleg007:
20160101 19:01:50
@anando_du same thing happened to me , your comment was helpful 

Abhinandan Agarwal:
20151018 20:39:53
N(log N)+M(log N)**3 solution gives TLE .. :\ 

Sudharsansai:
20150929 19:14:58
Learnt a lot .


Shahed Shahriar:
20150926 04:15:28
in c++(g++4.3.2) got WA and with the same code got AC in c++14 (g++5.1) 

Pulkit Singhal:
20150901 08:52:34
Persistent Segment Tree Nailed It :D 

anando_du:
20150722 12:05:51
used scanf() printf() got AC ..


ankit kumar:
20150703 16:29:21
!micro !soft=macro hard; hahaha nyc.. problem indeed!! 

i_am_looser:
20150610 16:56:38
persistent segment tree. Got AC using O(nlog(n)) ; ) 

gyosh:
20140119 15:09:58
Beautiful problem. There exists solution which run in O(log^3 N), O(log^2 N), and O(log N) per query. Explore them and learn something new!

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 