Problem:
Score: 300 points

Problem Statement

Takahashi has decided to hold fastest-finger-fast quiz games. Kizahashi, who is in charge of making the scoreboard, is struggling to write the program that manages the players' scores in a game, which proceeds as follows.

A game is played by N players, numbered 1 to N. At the beginning of a game, each player has K points.

When a player correctly answers a question, each of the other N-1 players receives minus one (-1) point. There is no other factor that affects the players' scores.

At the end of a game, the players with 0 points or lower are eliminated, and the remaining players survive.

In the last game, the players gave a total of Q correct answers, the i-th of which was given by Player A_i.
For Kizahashi, write a program that determines whether each of the N players survived this game.

Constraints

All values in input are integers.

2 \leq N \leq 10^5

1 \leq K \leq 10^9

1 \leq Q \leq 10^5

1 \leq A_i \leq N\ (1 \leq i \leq Q)

Input

Input is given from Standard Input in the following format:

N K Q
A_1
A_2
.
.
.
A_Q

Output

Print N lines. The i-th line should contain Yes if Player i survived the game, and No otherwise.

Sample Input 1

6 3 4
3
1
3
2

Sample Output 1

No
No
Yes
No
No
No

In the beginning, the players' scores are (3, 3, 3, 3, 3, 3).

Player 3 correctly answers a question. The players' scores are now (2, 2, 3, 2, 2, 2).

Player 1 correctly answers a question. The players' scores are now (2, 1, 2, 1, 1, 1).

Player 3 correctly answers a question. The players' scores are now (1, 0, 2, 0, 0, 0).

Player 2 correctly answers a question. The players' scores are now (0, 0, 1, -1, -1, -1).

Players 1, 2, 4, 5 and 6, who have 0 points or lower, are eliminated, and Player 3 survives this game.

Sample Input 2

6 5 4
3
1
3
2

Sample Output 2

Yes
Yes
Yes
Yes
Yes
Yes

Sample Input 3

10 13 15
3
1
4
1
5
9
2
6
5
3
5
8
9
7
9

Sample Output 3

No
No
No
No
Yes
No
No
No
Yes
No

Solution in Scala (2.11.7) (judge verdict: Time Limit Exceeded)

import scala.io.StdIn

object Main extends App {
  val Array(n, k, q)  = StdIn.readLine().split(" ").map(_.toInt)
  var a: Array[Int]  = Array.empty


  if ((k - q) > 0) {
    (1 to q).foreach { i =>
      a = a :+ StdIn.readLine().toInt
    }
    
    (1 to n).foreach {i =>
      println("Yes")
    }
  } else  {
    var cnt : scala.collection.mutable.Map[Int, Int] = scala.collection.mutable.Map.empty
    (1 to q).foreach { i =>
      val j =  StdIn.readLine().toInt
      //      println(cnt.contains(j))
      val v = cnt.getOrElse(j, 0)
      cnt += (j -> (v + 1))

//      println(cnt.mkString(" "))
    }


    (1 to n).map { i =>
      //        println("i: " + i)
      val condition = cnt.getOrElse(i, 0) + k - q
      if (condition > 0) "Yes" else "No"
    }.foreach { v => println(v) }
  }
}