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
mubtasim91:
20210118 22:37:18
My java code got accepted at first submission. Just merge sort tree + Binary search worked though it took over 7 seconds! 

kanishkverma_1:
20201124 12:37:39
Note : for java users Merge Sort Tree + BinarySearch Will give u tle on 16th Test case .


martins_:
20201015 01:31:42
Thanks for setting a Javafriendly time limit. 

nemesys:
20201014 15:14:27
No need for coordinade compression like some people are saying, binary searching the entire range works fine. 

yaseenmollik:
20200802 23:33:58
Solved using merge sort tree


tushar_ka:
20200802 15:56:12
Nice problem.


jopdhiwaala:
20200718 07:40:46
I feel so bad for messing it up so many times haha 

mhasan01:
20200714 02:27:35
Accepted using persistent segment tree :) 

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... 
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 