Problem:
Score : 600 points

Problem Statement

You are given an integer sequence A of length N and an integer K.
You will perform the following operation on this sequence Q times:

Choose a contiguous subsequence of length K, then remove the smallest element among the K elements contained in the chosen subsequence (if there are multiple such elements, choose one of them as you like).

Let X and Y be the values of the largest and smallest element removed in the Q operations. You would like X-Y to be as small as possible.
Find the smallest possible value of X-Y when the Q operations are performed optimally.

Constraints

1 \leq N \leq 2000

1 \leq K \leq N

1 \leq Q \leq N-K+1

1 \leq A_i \leq 10^9

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N K Q
A_1 A_2 ... A_N

Output

Print the smallest possible value of X-Y.

Sample Input 1

5 3 2
4 3 1 5 2

Sample Output 1

1

In the first operation, whichever contiguous subsequence of length 3 we choose, the minimum element in it is 1.
Thus, the first operation removes A_3=1 and now we have A=(4,3,5,2).
In the second operation, it is optimal to choose (A_2,A_3,A_4)=(3,5,2) as the contiguous subsequence of length 3 and remove A_4=2.
In this case, the largest element removed is 2, and the smallest is 1, so their difference is 2-1=1.

Sample Input 2

10 1 6
1 1 2 3 5 8 13 21 34 55

Sample Output 2

7

Sample Input 3

11 7 5
24979445 861648772 623690081 433933447 476190629 262703497 211047202 971407775 628894325 731963982 822804784

Sample Output 3

451211184

Solution in C++14 (GCC 5.4.1) (judge verdict: Accepted)

#include <limits>
using ll = long long;
constexpr int INF = std::numeric_limits<int>::max() / 2;
constexpr ll LNF = std::numeric_limits<ll>::max() / 2;

#include <bits/stdc++.h>
using namespace std;

template <typename T>
void print(vector<T> const &x, string s = "") {
}

ll compute(vector<ll> v, int K, int Q, vector<int> &seps) {
    int N = v.size();
    sort(seps.begin(), seps.end());
    seps.push_back(N);
    print(seps, "seps: ");
    for (int i = 1; i < (int)seps.size(); i++) {
        sort(v.begin() + seps[i - 1] + 1, v.begin() + seps[i]);
    }
    print(v, "sorted v: ");

    vector<ll> ans;
    ans.reserve(N);
    for (int i = 1; i < (int)seps.size(); i++) {
        ans.insert(ans.end(), v.begin() + seps[i - 1] + 1,
                   v.begin() + seps[i - 1] + 1 +
                       max(0, seps[i] - seps[i - 1] - 1 - K + 1));
    }
    print(ans, "ans: ");
    sort(ans.begin(), ans.end());
    seps.pop_back();
    return Q <= (int)ans.size() ? ans[Q - 1] - ans[0] : LNF;
}

int main() {
    int N, K, Q;
    cin >> N >> K >> Q;
    vector<ll> orig(N);
    for (int i = 0; i < N; i++) { cin >> orig[i]; }

    vector<pair<ll, int>> cp(N);
    for (int i = 0; i < N; i++) {
        cp[i].first  = orig[i];
        cp[i].second = i;
    }
    sort(cp.begin(), cp.end());

    vector<int> seps = {-1};
    ll mi            = compute(orig, K, Q, seps);
    for (auto const &p : cp) {
        seps.push_back(p.second);
        ll res = compute(orig, K, Q, seps);
        if (res == LNF) break; // ??????
        mi = min(mi, res);
    }
    cout << mi << endl;
    return 0;
}