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 Rust (1.42.0) (judge verdict: Accepted)

use proconio::input;

#[allow(unused_imports)]
use proconio::marker::{Bytes, Chars, Usize1};
#[allow(unused_imports)]
use std::cmp::*;
#[allow(unused_imports)]
use std::collections::*;
#[allow(unused_imports)]
use std::ops::*;
#[derive(Clone, Debug, Default)]
struct Struct;


// [l,h) の中でもっとも手前のfalseになる場所を探す. 全てのtrueはfalseより手前にある必要がある.
fn partition_point<F>(l0: usize, h0: usize, f: F) -> usize
where
    F: Fn(usize) -> bool,
{
    let mut l = l0;
    let mut h = h0;

    while h - l > 0 {
        let m = l + (h - l) / 2;
        if f(m) {
            l = m + 1;
        } else {
            h = m;
        }
    }
    return l;
}





fn is_possible(
    score: i64,
    n: usize,
    m: usize,
    v: usize,
    p: usize,
    a: &Vec<i64>,
    asum: &Vec<i64>,
) -> bool {
    if a[n - p] <= score {
        true
    } else if (score + m as i64) < a[n - p] {
        false
    } else {
        // 点数がscore以下の問題low個全てに、全員が1票を入れる
        // high=n-(p-1)以降の問題全てに、全員が1票を入れる
        // 間のhigh-low個の問題に、スコアがscore+m を超えないように残りの票(v-low-(p-1))*mを振り分けることができるか?
        let low = partition_point(0, n, |i| a[i] <= score);
        let high = n - (p - 1);
        let remain_votes_per_judge = v as i64 - low as i64 - (p - 1) as i64;
        if remain_votes_per_judge <= 0 {
            true
        } else {
            let capacity = (score + m as i64) * ((high - low) as i64) - (asum[high] - asum[low]);
            remain_votes_per_judge * m as i64 <= capacity
        }
    }
}

//#[proconio::fastout]
fn main() {
    input! {
        n:usize,
        m:usize,
        v:usize,
        p:usize,
        a_:[i64;n],
    }

    let mut a: Vec<i64> = a_;
    a.sort();
    let mut sum: i64 = 0;
    let mut asum = Vec::with_capacity(n + 1);
    asum.push(0);
    for x in &a {
        sum += *x as i64;
        asum.push(sum);
    }

    
    let mut ok: i64 = 1000000000i64;
    let mut ng: i64 = -1;


    while ok - ng > 1 {
        let middle = ng + (ok - ng) / 2;
        if is_possible(middle, n, m, v, p, &a, &asum) {
            ok = middle;
        } else {
            ng = middle;
        }
        //println!("ok={}, ng={}", ok, ng);
    }

    let l = partition_point(0, n, |i| a[i] < ok);
    println!("{}", n - l);
}