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
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

akshayv3: 2016-07-16 11:01:50

Solved using Persistent Segment trees and execution time was 0.5 s and the same solution times out in c++ 4.3.2

shiva_swag1: 2016-06-24 21:10:51

binary search +persistence segment tree..
binary search over -10^9 to +10^9 got tle..
binary search over elements of arr got ac..
log(2*10^9) factor proved very costly than log(10^5)... :-)

oleg007: 2016-01-01 19:01:50

@anando_du same thing happened to me , your comment was helpful

Abhinandan Agarwal: 2015-10-18 20:39:53

N(log N)+M(log N)**3 solution gives TLE .. :-\

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)


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