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).
Output
For each question output the answer to it — the kth number in sorted a[i ... j] segment.
Example
Input: 7 3 1 5 2 6 3 7 4 2 5 3 4 4 1 1 7 3 Output: 5 6 3
Note: a naive solution will not work!!!
hide comments
beefucurry:
20231020 23:16:08
Some (maybe all) of the input test cases use '\r\n' , watch out for that. Also the array elements can be negative in input tests, watch out for that too. 

vuduoc:
20231003 11:09:02
we dont need merge sort just use quick sort and segment tree you will get AC 

e_sasi:
20230914 00:03:05
merge sort tree is giving me TLE in C++.  _  

r_ash:
20230609 13:55:40
is there any test cases which could be giving me a WA, all my test cases that I tried seem correct


metalavocado99:
20230507 17:32:41
DANG ! I just bought the Darth Vader skin in Fortnite ! I am cool now 

blaze_sharp:
20230104 11:09:52
used wavelet tree and array value compression . got accepted , time taken 1s 

daukah_:
20221213 10:15:04
O(nlogn + mlog(2e9)lognlogn) 

rapiram31:
20221128 19:39:50
@fire5386 how the hell, its not working and won't work 

ppap_1264589:
20220902 10:59:26
O(NlogN + QlogN) using Persistent Segment Tree 

fuadul_hasan:
20220831 12:10:23
Easy merge sort tree + binary search problem Last edit: 20220831 12:10:39 
Added by:  psetter 
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 