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.util.Scanner;

// 単純に正解者以外を-1ポイントするとループが増えてTLEになるので、
// 正解に着目して敗退判定を工夫する
public class Main {

    public static void main(String[] args) {
        Scanner scanner = new Scanner(System.in);
        int N = Integer.parseInt(scanner.next());
        long K = Long.parseLong(scanner.next());
        int Q = Integer.parseInt(scanner.next());

        int[] A = new int[Q];

        for (int i = 0; i < Q; i++) {
            A[i] = Integer.parseInt(scanner.next());
        }
        scanner.close();

        long[] ansCount = new long[N];

        // 答えを処理していく
        for (int i = 0; i < Q; i++) {
            // 正解した人を++
            int correctIndex = A[i] - 1;
            ansCount[correctIndex]++;
        }

        // 0ポイント以下は敗退
        for (int i = 0; i < N; i++) {
            // 初期ポイント - 問題数 + 正解数 が 1以上であればOK
            boolean isWin = K - Q + ansCount[i] >= 1;
            System.out.println(isWin ? "Yes" : "No");
        }
    }
}