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
devarshi09:
20180503 06:15:15
O(log N)^3 works fine!


Jose Arias Perez [KIR@]:
20180305 02:17:42
Any tips on the MergeSort solution with O(lg^2N) per query ?? 

siva2697:
20180303 08:53:34
size of seg tree =2060964 AC :) 

sarwar__05:
20171219 13:56:43
Solve KQUERYO first. Last edit: 20171219 13:57:07 

newbie:
20171024 22:26:38
finally accepted,


AAKASH TYAGI:
20170813 21:29:57
O( log^3 n ) per query works fine. Just remember to binary search on array elements rather than the entire range. 

harsh_jain1:
20170810 19:43:35
Solved using trie...wow!!


nikolatech:
20170624 12:52:52
Last edit: 20180221 13:49:34 

Eddy Cael:
20170616 21:59:13
Hint: Maybe you will need to solve KQUERY first. using Segment Trees of course. 

shubham:
20170614 18:08:50
Qlog^3(n) doesn't work with fast input.. TLE 
Added by:  ~!(*(@*!@^& 
Date:  20090224 
Time limit:  0.115s0.667s 
Source limit:  50000B 
Memory limit:  1536MB 
Cluster:  Cube (Intel G860) 
Languages:  All except: ERL JSRHINO 
Resource:  Northeastern Europe 2004 Northern Subregion 