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 PHP (7.4.4) (judge verdict: Accepted)

<?php
list($n, $m, $v, $p) = ints();
$a = ints();
rsort($a);
$ok = $p - 1;
$ng = $n;
while (abs($ok - $ng) > 1) {
    $mid = intdiv($ok + $ng, 2);
    // mid に m 人全員が投票しても p 番目のスコアを超えない場合は採用される可能性なし
    if ($a[$mid] + $m < $a[$p - 1]) {
        $ng = $mid;
        continue;
    }
    // mid の採用の可能性に影響しない投票数を数える
    $cnt = 0;
    for ($i = 0; $i < $n; ++$i) {
        if ($i === $mid) continue;
        // 大きい順に p-1 個については全力投票してもok
        if ($i < $p - 1) $cnt += $m;
        // 残りについては a[mid]+m を超えない範囲の人数が投票してもok
        else $cnt += min($m, $a[$mid] + $m - $a[$i]);
    }
    if ($cnt >= $m * ($v - 1)) $ok = $mid;
    else $ng = $mid;
}
echo $ok + 1;
function ints()
{
    return array_map('intval', explode(' ', trim(fgets(STDIN))));
}