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.Generic;
using System.Diagnostics;
using System.IO;
using System.Linq;
using System.Text;

class Myon

{
    public Myon() { }
    public static int Main()
    {
        cin = new Scanner();
        new Myon().calc();
        return 0;
    }
    static Scanner cin;

    void calc()
    {
        int N = cin.nextInt();
        int M = cin.nextInt();
        int V = cin.nextInt();
        int P = cin.nextInt();
        long[] A = cin.ArrayLong(N);

        Array.Sort(A);

        int ok = N - 1; // ok can win
        int ng = -1; // ng can't win
        while(Math.Abs(ng - ok) > 1)
        {
            int mid = (ok + ng) / 2;
            if (check(A, N, M, V, P, mid)) ok = mid;
            else ng = mid;
        }
        Console.WriteLine(N - ok);
    }

    bool check(long[] A, int N, int M, int V, int P, int t)
    {
        int target = N - P;

        long sum = 0;
        long need = 0;

        int add = V - P;
        if (add < 0) add = 0;
        long needsum = add * M;


        for (int a = 0; a < target; a++)
        {
            int i = a;
            if (i >= t) i++;
            long diff = (A[t] + M) - A[i];
            //Console.WriteLine(t + " " + a + " " + diff);
            if (diff < 0) return false;
            need += Math.Min(M, diff);
        }
        //Console.WriteLine(need + " " + needsum + " " + V + " " + P + " " + needsum);

        return need >= needsum;
    }

}


class Scanner
{
    string[] s;
    int i;

    char[] cs = new char[] { ' ' };

    public Scanner()
    {
        s = new string[0];
        i = 0;
    }

    public string next()
    {
        if (i < s.Length) return s[i++];
        string st = Console.ReadLine();
        while (st == "") st = Console.ReadLine();
        s = st.Split(cs, StringSplitOptions.RemoveEmptyEntries);
        if (s.Length == 0) return next();
        i = 0;
        return s[i++];
    }

    public int nextInt()
    {
        return int.Parse(next());
    }
    public int[] ArrayInt(int N, int add = 0)
    {
        int[] Array = new int[N];
        for (int i = 0; i < N; i++)
        {
            Array[i] = nextInt() + add;
        }
        return Array;
    }

    public long nextLong()
    {
        return long.Parse(next());
    }

    public long[] ArrayLong(int N, long add = 0)
    {
        long[] Array = new long[N];
        for (int i = 0; i < N; i++)
        {
            Array[i] = nextLong() + add;
        }
        return Array;
    }

    public double nextDouble()
    {
        return double.Parse(next());
    }


    public double[] ArrayDouble(int N, double add = 0)
    {
        double[] Array = new double[N];
        for (int i = 0; i < N; i++)
        {
            Array[i] = nextDouble() + add;
        }
        return Array;
    }
}


class XRand
{
    uint x, y, z, w;


    public XRand()
    {
        init();
    }

    public XRand(uint s)
    {
        init();
        init_xor128(s);
    }

    void init()
    {
        x = 314159265; y = 358979323; z = 846264338; w = 327950288;

    }

    public void init_xor128(uint s)
    {
        z ^= s;
        z ^= z >> 21; z ^= z << 35; z ^= z >> 4;
        z *= 736338717;
    }

    uint next()
    {
        uint t = x ^ x << 11; x = y; y = z; z = w; return w = w ^ w >> 19 ^ t ^ t >> 8;
    }

    public long nextLong(long m)
    {
        return (long)((((ulong)next() << 32) + next()) % (ulong)m);
    }

    public int nextInt(int m)
    {
        return (int)(next() % m);
    }

    public int nextIntP(int a)
    {
        return (int)Math.Pow(a, nextDouble());
    }

    public int nextInt(int min, int max)
    {
        return min + nextInt(max - min + 1);
    }


    public double nextDouble()
    {
        return (double)next() / uint.MaxValue;
    }

    public double nextDoubleP(double a)
    {
        return Math.Pow(a, nextDouble());
    }
}