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
aryan__0406:
20200528 19:02:48
@maruf_hasan refer to geeksforgeeks article on merge sort tree and thank me later.


maruf_hasan:
20200503 03:19:12
Can anybody explain how to apply the binary search on merge sort tree here?and why the binary search will work here??TIA... 

santhosh_80:
20200427 15:17:22
Worked with sqrt decomposition 

Sarthak Agarwal:
20200402 16:19:46
Used Merge Sort tree, AC in 1 go! 

itssanat:
20200401 09:10:18
segment tree with vectors and binary search :) 

kesh4281:
20200324 09:07:34
no.s can be ve, beware


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.

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 