MKTHNUM - K-th Number


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 k-th 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 k-th 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 k-th number in sorted 
a[i ... j] segment. 

SAMPLE OUTPUT
5
6
3
Note : naive solution will not work!!!

hide comments
rituraj2847: 2018-09-05 14:14:33

Print '-1' if there's no kth number.

kkislay20: 2018-07-02 09:22:38

I am getting TLE..could someone help me out https://ideone.com/v9UzfI
I used merge sort with O(N*2 (logn)*2 ) sol

devarshi09: 2018-05-03 06:15:15

O(log N)^3 works fine!
Solved with Merge Sort tree!

Jose Arias Perez [KIR@]: 2018-03-05 02:17:42

Any tips on the MergeSort solution with O(lg^2N) per query ??

siva2697: 2018-03-03 08:53:34

size of seg tree =2060964 AC :)

sarwar__05: 2017-12-19 13:56:43

Solve KQUERYO first.

Last edit: 2017-12-19 13:57:07
newbie: 2017-10-24 22:26:38

finally accepted,
A few tips:
1. numbers can be +ve, -ve and 0.
2. Use Fast I/O Got many tle because of that.

Thanks to @harsh_jain1 for giving the hint that it can be solved using trie also.

AAKASH TYAGI: 2017-08-13 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: 2017-08-10 19:43:35

Solved using trie...wow!!

nikolatech: 2017-06-24 12:52:52

Last edit: 2018-02-21 13:49:34

Added by:~!(*(@*!@^&
Date:2009-02-24
Time limit:0.115s-0.667s
Source limit:50000B
Memory limit:1536MB
Cluster: Cube (Intel G860)
Languages:All except: ERL JS-RHINO
Resource:Northeastern Europe 2004 Northern Subregion