Problem:
Score : 700 points

Problem Statement

N problems are proposed for an upcoming contest. Problem i has an initial integer score of A_i points.

M judges are about to vote for problems they like. Each judge will choose exactly V problems, independently from the other judges,
and increase the score of each chosen problem by 1.

After all M judges cast their vote, the problems will be sorted in non-increasing order of score, and the first P problems will be chosen for the problemset.
Problems with the same score can be ordered arbitrarily, this order is decided by the chief judge.

How many problems out of the given N have a chance to be chosen for the problemset?

Constraints

2 \le N \le 10^5

1 \le M \le 10^9

1 \le V \le N - 1

1 \le P \le N - 1

0 \le A_i \le 10^9

Input

Input is given from Standard Input in the following format:

N M V P
A_1 A_2 ... A_N

Output

Print the number of problems that have a chance to be chosen for the problemset.

Sample Input 1

6 1 2 2
2 1 1 3 0 2

Sample Output 1

5

If the only judge votes for problems 2 and 5, the scores will be 2 2 1 3 1 2.
The problemset will consist of problem 4 and one of problems 1, 2, or 6.

If the only judge votes for problems 3 and 4, the scores will be 2 1 2 4 0 2.
The problemset will consist of problem 4 and one of problems 1, 3, or 6.

Thus, problems 1, 2, 3, 4, and 6 have a chance to be chosen for the problemset. On the contrary, there is no way for problem 5 to be chosen.

Sample Input 2

6 1 5 2
2 1 1 3 0 2

Sample Output 2

3

Only problems 1, 4, and 6 have a chance to be chosen.

Sample Input 3

10 4 8 5
7 2 3 6 1 6 5 4 6 5

Sample Output 3

8

Solution in Java8 (OpenJDK 1.8.0) (judge verdict: Wrong Answer)

import java.io.*;
import java.io.IOException;
import java.util.*;

@SuppressWarnings({"rawtypes", "unchecked"})
class Main {
    final static int INF = 1 << 28;
    final static long LNF = 1L << 60;
    final static double EPS = 1e-9;
    final static double GOLDEN_RATIO = (1.0 + Math.sqrt(5)) / 2.0;

    static final long MOD = 1_000_000_007;

    public static void main(String[] args) throws Exception {
        // long start = System.currentTimeMillis();
        final MyScanner sc = new MyScanner();
        int N;
        N = sc.nextInt();
        int M;
        M = sc.nextInt();
        int V;
        V = sc.nextInt();
        int P;
        P = sc.nextInt();
        int[] A = new int[(int)(N)];
        for(int i = 0 ; i < N ; i++){
                A[i] = sc.nextInt();
        }
        solve(N, M, V, P, A);
        // long end = System.currentTimeMillis();
        // System.out.println((end - start)  + "ms");
    }

    static void solve(int N, int M, int V, int P, int[] A){
        HashMap<Integer, Integer> hashmap = new HashMap<>();

        for (int l : A) {
            if(hashmap.containsKey(l)) hashmap.put(l, hashmap.get(l) + 1);
            else hashmap.put(l, 1);
        }

        TreeSet<Integer> ts = new TreeSet(hashmap.keySet());
        
        int v;
        int n_v;
        int n_sum = 0;
        int v_border = -1;
        int ans = 0;
        int fix = 0;

        while(!ts.isEmpty()) {
            v = ts.pollLast();
            n_v = hashmap.get(v);
            n_sum += n_v;

            if(n_sum < P) {
                ans = n_sum;
            } else {
                if(v_border < 0) v_border = v;
                fix += (v_border - v) * n_v;

                int n_vote = (V - (N - n_sum + (P - 1))) * M;
                int n_fixed_vote = n_vote - fix;
                if(v + M < v_border) {
                    break;
                } else if(n_fixed_vote < 0) {
                    ans = n_sum;
                } else {
                    int delta = (int)Math.ceil(1.0 * n_fixed_vote / (n_sum - P + 1));
                    if(v + M >= v_border + delta) ans = n_sum;
                    else break;
                }
            }
        }
        System.out.println(ans);

    }

    static class MyScanner {
 
        BufferedReader br;
        StringTokenizer st;
 
        MyScanner(FileReader fileReader) {
            br = new BufferedReader(fileReader);
        }
 
        MyScanner() {
            br = new BufferedReader(new InputStreamReader(System.in));
        }
 
        String nn() {
            while (st == null || !st.hasMoreElements()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }
 
        String next() {
            String ans = "";
            try {
                ans = br.readLine();
            } catch (IOException ex) {
                ex.printStackTrace();
            }
            return ans;
        }
 
        char nextChar() {
            return nn().charAt(0);
        }
 
        int nextInt() {
            return Integer.parseInt(nn());
        }
 
        long nextLong() {
            return Long.parseLong(nn());
        }
 
        double nextDouble() {
            return Double.parseDouble(nn());
        }
 
        Integer[] niArr0(int n) {
            Integer[] ar = new Integer[n];
            for (int i = 0; i < n; i++) {
                ar[i] = nextInt();
            }
            return ar;
        }
 
        Integer[] niArr1(int n) {
            Integer[] ar = new Integer[n + 1];
            for (int i = 1; i <= n; i++) {
                ar[i] = nextInt();
            }
            return ar;
        }
 
        Long[] nlArr0(int n) {
            Long[] ar = new Long[n];
            for (int i = 0; i < n; i++) {
                ar[i] = nextLong();
            }
            return ar;
        }
 
        Long[] nlArr1(int n) {
            Long[] ar = new Long[n + 1];
            for (int i = 1; i <= n; i++) {
                ar[i] = nextLong();
            }
            return ar;
        }
    }
}