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
Eddy Cael: 2017-06-16 21:59:13

Hint: Maybe you will need to solve KQUERY first. using Segment Trees of course.

shubham: 2017-06-14 18:08:50

Qlog^3(n) doesn't work with fast input.. TLE

ksmukta: 2017-06-14 13:35:00

Did you know that naive solution of 'tourist' was accepted.

free__bird: 2017-06-12 08:35:20

took me 2 days to learn the concept of persistent tree,finally AC :) in one go.
read the tutorial of anudeep on persistent segment tree again and again and you will get the concept.
After it must try the CLONEME problem on Codechef.

barishnamazov: 2017-06-11 13:44:39

why O((n + m)log^2(n)) doesn't get tle?

mridul1809: 2017-06-08 22:44:19

persistent segment tree...amazing DS :D

sfialok98: 2017-06-06 21:16:24

Finally Accepted,Learned Persistent Segment Trees....!!!!
What a beauiful data structure..!! :-)

joseluisacv2: 2017-06-06 03:01:15

The number of queries is wrong. It is M<= 1e5

leafbebop: 2017-05-31 05:16:35

Note: sometimes it is not the algorithms blocks you from AC, but the I/O speed.
For golang user, read this topic: https://groups.google.com/forum/#!topic/golang-nuts/W08rFBcHKbc
Other language may have similar issues. Try Buffered I/O.

Oh, and also, minimize function calls, of course.

Last edit: 2017-05-31 05:20:11
mddaud001: 2017-05-20 21:26:13

Trying to solve from last week
Merge sort tree + Compression + Binary_search AC :-)


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
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