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 C# (Mono 4.6.2.0) (judge verdict: Wrong Answer)

using System;
using System.Collections;
using System.Collections.Generic;
using System.Diagnostics;
using System.IO;
using System.Linq;
using System.Numerics;
using System.Text;
using System.Text.RegularExpressions;
using System.Threading.Tasks;
using static System.Math;
using MethodImplAttribute = System.Runtime.CompilerServices.MethodImplAttribute;
using MethodImplOptions = System.Runtime.CompilerServices.MethodImplOptions;

public static class P
{
    public static void Main()
    {
        var nmvp = Console.ReadLine().Split().Select(int.Parse).ToArray();
        var n = nmvp[0];
        var m = nmvp[1];
        var v = nmvp[2];
        var p = nmvp[3];
        var a = Console.ReadLine().Split().Select(long.Parse).OrderByDescending(x => x).ToArray();
        //m回v個 +1 最終的にtop p
        //単調性があるため二分探索可能
        var valid = 0;
        var invalid = n;
        while (invalid - valid > 1)
        {
            var mid = (valid + invalid) / 2;
            if (mid.CanAdopt(a, m, v, p)) valid = mid;
            else invalid = mid;
        }
        Console.WriteLine(invalid);
    }
    static bool CanAdopt(this int ind, long[] problems, int m, int v, int p)
    {
        long maxScore = problems[ind] + m;
        v--;
        int i = 0;

        //targetより大きいのがp個以上あったら

        for (; i < problems.Length; i++)
            if (problems[i] <= maxScore) break;
        
        int largeProblemCount = i;
        if (p <= largeProblemCount) return false;
        //target以上のには投票して構わない=投票回数を個数分減らせる
        v -= largeProblemCount;
        
        //問題はp以下の雑魚 とりあえず最初の複数個は全部埋める 上がp-1個になった瞬間終わり
        for (; i < problems.Length && largeProblemCount < p - 1 && 0 < v; i++)
        {
            if (ind == i) continue;
            if (maxScore < problems[i] + m) largeProblemCount++;
            v--;
        }
        long votes = 0;
        //pに揃える
        for (; i < problems.Length; i++)
        {
            if (ind == i) continue;
            votes += Min(m, Max(0, maxScore - problems[i]));
        }
        return m * v <= votes;
    }
}