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
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.
The first line of the input file contains n --- the size of the
array, and m --- the number of questions to answer (1 <= n <= 100
000, 1 <= m <= 5 000).
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
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).
For each question output the answer to it --- the k-th number in sorted a[i...j] segment.
Sample Input
7 3 1 5 2 6 3 7 4 2 5 3 4 4 1 1 7 3Sample Output
5 6 3Hint
This problem has huge input,so please use c-style input(scanf,printf),or you may got time limit exceed.
之前用网上的一些模板水了这道题，这道题做法真心很多：归并树、平衡树（感觉要套上莫队？）、主席树。从时空复杂度的角度来说，主席树无疑最优。据同校大佬TJW说，主席树可以不离散化，支持在线，方法是预先准备好值域大小的线段树（这棵线段树是假的，因为一个结点都没有），由于每次插入一个数至多更新logn个结点，所以每当进入一个还没有开的区间时就开一下，完全不用担心会炸：就算值域是[-2e18,2e18]，外面套一个log就变成了60，与离散化线段树的大约是20的log差距不大。