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: Runtime Error)

import java.util.Scanner

object Main {
  def inProc(sc: Scanner): (Int, Int, Int, List[Int]) = {
    val n = sc.nextInt()
    val k = sc.nextInt()
    val q = sc.nextInt()
    var a: List[Int] = Nil
    for(_ <- 0 until q) a = sc.nextInt() :: a
    (n, k, q, a)
  }
  def outProc(ans: List[String]): Unit = {
    ans.foreach(e => println(e))
  }
  def solve(tuple: (Int, Int, Int, List[Int])): List[String] = {
    tuple match{
      case (n, k, q, a) => solveMain(n, k, q, a)
    }
  }
  def solveMain(n: Int, k: Int, q: Int, a: List[Int]): List[String] = {
    var ans: List[String] = Nil
    for(i <- 1 to n) {
      if(a.foldLeft(0){case (sum, e) if (e == i) => sum + 1} + k - q > 0) ans = "Yes" :: ans
      else ans = "No" :: ans
    }
    ans.reverse
  }
  def main(args: Array[String]): Unit = {
    outProc(solve(inProc(new Scanner(System.in))))
  }
}