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
ab_biswas09: 2019-03-16 20:11:15

Finally AC

kukreja_vlk: 2019-03-09 04:27:35

Any solutions in Java ? Getting TLE after some cases

gormint7777: 2019-03-05 19:21:50

weak test cases!!

nik7: 2019-02-18 06:42:01

@newbie how it can be solved using trie. Can you please explain

alucard_01: 2018-12-19 15:04:12

cool sum..!!

kspoj: 2018-12-07 18:23:11

My first persistent seg tree prob.. Yay :D

tien0903: 2018-11-22 12:31:34

awesome problems =)) and very nice persistant IT too . it's a amazing :v

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!


Added by:~!(*(@*!@^&
Date:2009-02-24
Time limit:0.115s-0.667s
Source limit:50000B
Memory limit:1536MB
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