MKTHNUM.cpp

/*
	By Anudeep Nekkanti
	Editorial at www.blog.anudeep.com/persistent-segment-trees-explained-with-spoj-problems
	Question at http://www.spoj.com/problems/MKTHNUM/
	O( (N+M) * log N )
*/

#include <cstdio>
#include <map>
#include <vector>
#include <cstring>
using namespace std;

#define sz size()
#define pb push_back
#define rep(i,n) for(int i=0;i<n;i++)
#define fd(i,a,b) for(int i=a; i>=b; i--)

#define N 111111

struct node
{
	int count;
	node *left, *right;

	node(int count, node *left, node *right):
		count(count), left(left), right(right) {}

	node* insert(int l, int r, int w);
};

node *null = new node(0, NULL, NULL); //see line 135

node * node::insert(int l, int r, int w)
{
	if(l <= w && w < r)
	{
		// With in the range, we need a new node
		if(l+1 == r)
		{
			return new node(this->count+1, null, null);
		}

		int m = (l+r)>>1;

		return new node(this->count+1, this->left->insert(l, m, w), this->right->insert(m, r, w));
	}

	// Out of range, we can use previous tree node.
	return this;
}

int query(node *a, node *b, int l, int r, int k)
{
	if(l+1 == r)
	{
		return l;
	}

	int m = (l+r)>>1;
	int count = a->left->count - b->left->count;
	if(count >= k)
		return query(a->left, b->left, l, m, k);

	return query(a->right, b->right, m, r, k-count);
}

int a[N], RM[N];
node *root[N];
int main()
{
	int n, m;
	scanf("%d%d", &n, &m);

	map <int, int> M;
	rep(i, n)
	{
		scanf("%d", &a[i]);
		M[a[i]];
	}

	int maxi = 0;

	for(map <int, int> :: iterator it = M.begin(); it != M.end(); it++)
	{
		M[it->first] = maxi;
		RM[maxi] = it->first;
		maxi++;
	}

	null->left = null->right = null;
	rep(i, n)
	{
		// Build a tree for each prefix using segment tree of previous prefix
		root[i] = (i == 0 ? null : root[i-1])->insert( 0, maxi, M[a[i]] );
	}

	while(m--)
	{
		int u, v, k;
		scanf("%d%d%d", &u, &v, &k);
		u--; v--;

		int ans = query(root[v], (u==0?null:root[u-1]), 0, maxi, k);
		printf("%d\n", RM[ans]);
	}
}