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).

Output

For each question output the answer to it — the k-th number in sorted a[i ... j] segment.

Example

Input:
7 3
1 5 2 6 3 7 4
2 5 3
4 4 1
1 7 3

Output:
5
6
3

Note: a naive solution will not work!!!


hide comments
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

[Edited by EB]
M <= 5000 is true.

Last edit: 2017-09-02 01:23:22
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 :-)

rihaz_zahir: 2017-02-15 20:12:33

why array compression with sqrt decomposition + segment tree is giving tle?

crazymax: 2016-10-31 15:01:26

Mo+ordered_set_tree (complexity with - Q*sqrt(N)*log(N)+N*sqrt(N)) solution gives TLE. :(

Ravi kumar: 2016-10-25 15:57:06

Increase time limit for java. there is not even a single accepted solution.
using (n+m)*logn complexity algo.

Edit: i tried the same algo in C++ and it passed. you need to increase time limit for java.

Last edit: 2016-10-25 16:17:58
i_m_a_coder: 2016-09-07 22:35:48

i did it using vectors and iterators bt getting wrong answer!!!

tamionv: 2016-08-27 03:56:22

I think I'm the first one to solve it in O((N+Q) * sqrt(N)) :)

kiwi1995: 2016-07-21 08:08:37

learnt a lot from this problem...:D


Added by:psetter
Date:2009-02-24
Time limit:1s
Source limit:50000B
Memory limit:1536MB
Cluster: Cube (Intel G860)
Languages:All except: ERL JS-RHINO
Resource:Northeastern Europe 2004 Northern Subregion