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++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include <iostream>
#include <cstdio>
#include <string>
#include <cstring>
#include <deque>
#include <list>
#include <queue>
#include <stack>
#include <vector>
#include <utility>
#include <algorithm>
#include <map>
#include <set>
#include <complex>
#include <cmath>
#include <limits>
#include <climits>
#include <ctime>
#include <cassert>
#include <numeric>
#include <functional>
#include <bitset>

using namespace std;
using lint = long long int;
long long int INF = 1001001001001001LL;
int inf = 1000000007;
long long int MOD = 1000000007LL;
double PI = 3.1415926535897932;
long long int di[] = {-1, 0, 1, 0, -1, 1, 1, -1};
long long int dj[] = {0, 1, 0, -1, 1, 1, -1, -1};

template<typename T1,typename T2>inline void chmin(T1 &a,const T2 &b){if(a>b) a=b;}
template<typename T1,typename T2>inline void chmax(T1 &a,const T2 &b){if(a<b) a=b;}

#define ALL(a) a.begin(),a.end()
#define RALL(a) a.rbegin(),a.rend()

/* do your best */

int main() {
  
  lint n, m, v, p; cin >> n >> m >> v >> p;
  vector<lint> a(n);
  for(int i = 0; i < n; i++) cin >> a[i];
  sort(RALL(a));
  
  lint lb = p - 1;
  lint ub = n;
  while(ub - lb > 1) {
    lint mid = (ub + lb) / 2;
    cerr << "mid = " << mid << endl;
    lint limit = a[mid] + m;
    lint cnt = v - p;

    vector<lint> vv;
    for(int i = p - 1; i < n; i++) {
      if(i == mid) continue;
      vv.push_back(a[i]);
    }
    cerr << "vv: " << endl;
    for(int i = 0; i < vv.size(); i++) cerr << vv[i] << " ";
    cerr << endl;

    // m 回やんなきゃ
    sort(ALL(vv));
    vector<int> ex;
    // cerr << "cnt = " << cnt << endl;
    // assert(cnt <= (int)vv.size());
    if(cnt <= 0) {
      // cerr << "mid = " << mid << endl;
      // cerr << "limit = " << limit << endl;
      // cerr << "v[0] = " << v[0] << endl;
      // cerr << "v.back() = " << v.back() << endl;
      // cerr << "boolean : " << (limit >= v.back()) << endl;
      if(limit >= vv.back()) lb = mid;
      else ub = mid;
      continue;
    }

    vector<lint> res;
    for(int i = 0; i < cnt; i++) {
      if(vv[i] + m > limit) {
        ex.push_back(vv[i] + m - limit);
      } else {
        res.push_back(limit - vv[i] - m);
      }
    }

    for(int i = cnt + 1; i < vv.size(); i++) {
      res.push_back(limit - vv[i]);
    }


    
    cerr << "limit = " << limit << endl;
    cerr << "ex: " << endl;

    bool ok = true;
    sort(ALL(res));
    for(int i = 0; i < res.size(); i++) {
      if(res[i] < 0) ok = false;
    }

    if(!ok) {
      ub = mid;
      continue;
    }
    if(res.size() < ex.size()) {
      ok = false;
    }

    if(!ok) {
      ub = mid;
      continue;
    }
    for(int i = 0; i < ex.size(); i++) {
      if(res[i] < ex[i]) ok = false;
    }

    if(ok) lb = mid;
    else ub = mid;
  }
  
  while(lb < n - 1) {
    if(a[lb + 1] == a[lb]) lb++;
    else break;
  }

  cout << lb + 1 << endl;

  
  return 0;
}