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
zufius:
20200201 15:09:50
this problem is easier than (& similar) problem COT (use persistent IT to solve) Last edit: 20200201 15:10:14 

fardin_abir:
20191220 09:28:54
solved it on O(log^3 * N).... nice problem... 

piasroy071:
20191021 20:11:07
Somehow my solution of merge sort tree with O(log^3 * N) got AC in 1.04s, although the time limit is 0.115s0.667s. Can someone explain this?


zhaopeng:
20190520 12:25:28
Merge Seg + Binary Search + compress(TLE if without), AC.


caro_linda2018:
20190426 02:16:28
ACed it in one go :) Last edit: 20190426 02:17:03 

golu20174024:
20190321 03:47:47
use persistent segment tree and ith order statistics


ab_biswas09:
20190316 20:11:15
Finally AC 

kukreja_vlk:
20190309 04:27:35
Any solutions in Java ? Getting TLE after some cases 

gormint7777:
20190305 19:21:50
weak test cases!!


nik7:
20190218 06:42:01
@newbie how it can be solved using trie. Can you please explain 
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 