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: Accepted)

import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;

public class Main {
	public static void main(String[] args) throws Throwable {
		MyScanner sc = new MyScanner();
		String nkq = sc.nextString();
		String[] nkqArr = nkq.split(" ");
		int n = Integer.parseInt(nkqArr[0]);
		int k = Integer.parseInt(nkqArr[1]);
		int q = Integer.parseInt(nkqArr[2]);

		// N人のスコア(0始まり注意)
		int[] scores = new int[n];
		// 最初の持ち点としてKではなく0を設定
		for (int i = 0; i < n; i++) {
			scores[i] = 0;
		}

		// Q行分ループ
		for (int i = 0; i < q; i++) {
			int winner = sc.nextInt();
			// (正解者の番号-1)に1加算
			int before = scores[winner - 1];
			scores[winner - 1] = before + 1;
		}

		// N人分ループ
		for (int i = 0; i < n; i++) {
			int result = scores[i];
			if (k > q - result) {
				// 点数 > 誤答数(=問題数 - 正解数)
				System.out.println("Yes");
			} else {
				System.out.println("No");
			}
		}
	}

	static class MyScanner {

		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));

		public String nextString() throws IOException {
			return br.readLine();
		}

		public int nextInt() throws NumberFormatException, IOException {
			return Integer.parseInt(nextString());
		}

		public String[] nextStringArr() throws IOException {
			return nextString().split(" ");
		}

		public Integer[] nextIntArr() throws IOException {
			String[] strArr = nextStringArr();
			Integer[] intArr = new Integer[strArr.length];
			for (int i = 0; i < strArr.length; i++) {
				intArr[i] = Integer.parseInt(strArr[i]);
			}
			return intArr;
		}
	}

}