Description
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.
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 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 109 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).
The second line contains n different integer numbers not exceeding 109 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.
Sample Input
7 3
1 5 2 6 3 7 4
2 5 3
4 4 1
1 7 3
Sample Output
5
6
3
Hint
This problem has huge input,so please use c-style input(scanf,printf),or you may got time limit exceed.
Source
Northeastern Europe 2004, Northern Subregion
题目大意：给出长度为n的序列和m个形如(i,j,k)的询问，询问区间[i,j]中第k大的数。
本题是经典的主席树（可持久化线段树）模板题，时间复杂度O(mlog2n)，空间复杂度O(nlog2n)。
1 program rrr(input,output); 2 type 3 treetype=record 4 lc,rc,s:longint; 5 end; 6 var 7 a:array[0..100010*30]of treetype; 8 rot,idx,b,c:array[0..100010]of longint; 9 n,m,i,cnt,l,r,j,k,mid,x,y,t:longint; 10 procedure sort(q,h:longint); 11 var 12 i,j,x,t:longint; 13 begin 14 i:=q;j:=h;x:=b[(i+j)>>1]; 15 repeat 16 while b[i]<x do inc(i); 17 while x<b[j] do dec(j); 18 if i<=j then 19 begin 20 t:=b[i];b[i]:=b[j];b[j]:=t; 21 t:=idx[i];idx[i]:=idx[j];idx[j]:=t; 22 inc(i);dec(j); 23 end; 24 until i>j; 25 if j>q then sort(q,j); 26 if i<h then sort(i,h); 27 end; 28 procedure build(k,l,r:longint); 29 var 30 mid:longint; 31 begin 32 a[k].s:=0; 33 if l=r then exit; 34 mid:=(l+r)>>1; 35 inc(cnt);a[k].lc:=cnt;build(cnt,l,mid); 36 inc(cnt);a[k].rc:=cnt;build(cnt,mid+1,r); 37 end; 38 procedure add(x:longint); 39 begin 40 inc(cnt);rot[i]:=cnt; 41 j:=cnt;k:=rot[i-1];a[j].s:=a[k].s+1; 42 l:=1;r:=n; 43 while l<r do 44 begin 45 mid:=(l+r)>>1;inc(cnt); 46 if x>mid then 47 begin 48 l:=mid+1; 49 a[j].lc:=a[k].lc;k:=a[k].rc; 50 a[j].rc:=cnt;j:=cnt;a[j].s:=a[k].s+1; 51 end 52 else 53 begin 54 r:=mid; 55 a[j].rc:=a[k].rc;k:=a[k].lc; 56 a[j].lc:=cnt;j:=cnt;a[j].s:=a[k].s+1; 57 end; 58 end; 59 end; 60 function ask(x,y,t:longint):longint; 61 begin 62 j:=rot[x-1];k:=rot[y];l:=1;r:=n;cnt:=0; 63 while l<r do 64 begin 65 mid:=(l+r)>>1; 66 if cnt+a[a[k].lc].s-a[a[j].lc].s>=t then begin r:=mid;j:=a[j].lc;k:=a[k].lc; end 67 else begin cnt:=cnt+a[a[k].lc].s-a[a[j].lc].s;l:=mid+1;j:=a[j].rc;k:=a[k].rc; end; 68 end; 69 exit(b[l]); 70 end; 71 begin 72 assign(input,'r.in');assign(output,'r.out');reset(input);rewrite(output); 73 readln(n,m); 74 for i:=1 to n do begin read(b[i]);idx[i]:=i; end; 75 sort(1,n); 76 for i:=1 to n do c[idx[i]]:=i; 77 cnt:=1;rot[0]:=1; 78 build(1,1,n); 79 for i:=1 to n do add(c[i]); 80 //for i:=1 to 40 do writeln(a[rot[i]].s); 81 for i:=1 to m do begin readln(x,y,t);writeln(ask(x,y,t)); end; 82 close(input);close(output); 83 end.