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
Sudharsansai: 2015-09-29 19:14:58

Learnt a lot .
Merge Sort Tree : O((N+M)*lgN*lgN)
Persistent Segment Tree : O((N+M)*lgN)

Shahed Shahriar: 2015-09-26 04:15:28

in c++(g++4.3.2) got WA and with the same code got AC in c++14 (g++5.1)

Pulkit Singhal: 2015-09-01 08:52:34

Persistent Segment Tree Nailed It :D

anando_du: 2015-07-22 12:05:51

used scanf() printf() got AC ..
used getchar_unlocked() , putchar_unlocked() got wa O.o
btw nice one !

ankit kumar: 2015-07-03 16:29:21

!micro !soft=macro hard; hahaha nyc.. problem indeed!!

i_am_looser: 2015-06-10 16:56:38

persistent segment tree. Got AC using O(nlog(n)) ; )

gyosh: 2014-01-19 15:09:58

Beautiful problem. There exists solution which run in O(log^3 N), O(log^2 N), and O(log N) per query. Explore them and learn something new!

not as beautiful as you

Last edit: 2015-04-03 01:00:56

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