Voting Judges

AtCoder

IDagc041_b

Time2000ms

Memory256MB

Difficulty—

$N$ 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: $N$ $M$ $V$ $P$ $A_1$ $A_2$ $...$ $A_N$ [samples]

Samples

Input #1

6 1 2 2
2 1 1 3 0 2

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.

Input #2

6 1 5 2
2 1 1 3 0 2

Output #2

3

Only problems $1$, $4$, and $6$ have a chance to be chosen.

Input #3

10 4 8 5
7 2 3 6 1 6 5 4 6 5

Output #3

API Response (JSON)

{
  "problem": {
    "name": "Voting Judges",
    "description": {
      "content": "$N$ 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 $V$ pro",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "agc041_b"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "$N$ problems are proposed for an upcoming contest. Problem $i$ has an initial integer score of $A_i$ points.\n$M$ judges are about to vote for problems they like. Each judge will choose exactly $V$ pro...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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