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!!!


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

hide comments
2024-10-09 07:44:01
coordinate compresion + partition segmentree
2023-10-20 23:16:08
Some (maybe all) of the input test cases use '\r\n' , watch out for that. Also the array elements can be negative in input tests, watch out for that too.
2023-10-03 11:09:02
we dont need merge sort just use quick sort and segment tree you will get AC
2023-09-14 00:03:05
merge sort tree is giving me TLE in C++. - _ -
2023-06-09 13:55:40
is there any test cases which could be giving me a WA, all my test cases that I tried seem correct
2023-05-07 17:32:41
DANG ! I just bought the Darth Vader skin in Fortnite ! I am cool now
2023-01-04 11:09:52
used wavelet tree and array value compression . got accepted , time taken 1s
2022-12-13 10:15:04
O(nlogn + mlog(2e9)lognlogn)
2022-11-28 19:39:50
@fire5386 how the hell, its not working and won't work
2022-09-02 10:59:26
O(NlogN + QlogN) using Persistent Segment Tree
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