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 Java8 (OpenJDK 1.8.0) (judge verdict: Wrong Answer)

import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.StringTokenizer;
import java.util.stream.IntStream;

class Main {
	
    public static void main(String[] args) {
		OriginScanner os = new OriginScanner();
		PrintWriter pw = new PrintWriter(System.out);
		
		int n = os.nextInt();
		int k = os.nextInt();
		int q = os.nextInt();
		
		int[] points = new int[n];
		
		for (int i = 0; i < q; i++) {
			points[os.nextInt() - 1]++;
		}
		pw.println(Arrays.toString(points));
		IntStream.of(points).forEach(p ->{
			if (p - (q - k) < 1) pw.println("No");
			else pw.println("Yes");
		});
		pw.close();
	}
    
	static class OriginScanner {
		StringTokenizer token;
		BufferedReader br;
		
		public OriginScanner() {
			br = new BufferedReader(new InputStreamReader(System.in));
		}
		
		String nextLine() {
			String str = null;
			try {
				str = br.readLine();
			}
			catch (IOException e) {
				System.out.println(e);
			}
			return str;
		}
		
		String next() {
			while (token == null || !token.hasMoreElements()) { 
				token = new StringTokenizer(nextLine());
			}
			return token.nextToken();
		}
		
		int nextInt() {
			return Integer.parseInt(next());
		}
		
		long nextLong() {
			return Long.parseLong(next());
		}
	}
}