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 C# (Mono 4.6.2.0) (judge verdict: Accepted)

using System;

public class Program
{
    static long n;
    static long k;
    static long q;
    static long[] a;

    static string output;

    static long[] score;

    public static void Main(string[] args)
    {
        Input();
        Proc();
        Output();
    }

    static void Input()
    {
        string[] input = null;

        // スペース区切りの整数の入力
        input = Console.ReadLine().Split(' ');
        n = long.Parse(input[0]);
        k = long.Parse(input[1]);
        q = long.Parse(input[2]);

        // スペース区切りの整数の入力
        a = new long[q];
        for (long idx = 0; idx < q; idx++)
        {
            input = Console.ReadLine().Split(' ');
            a[idx] = long.Parse(input[0]);
        }
    }

    static void Proc()
    {
        // スコア初期化
        score = new long[n];
        for (long idx = 0; idx < n; idx++)
        {
            score[idx] = k - q;
        }

        // 回答
        for (long idxA = 0; idxA < q; idxA++)
        {
            long idxAnswer = a[idxA] - 1;

            score[idxAnswer]++;
        }
    }

    static void Output()
    {
        for (long idxScore = 0; idxScore < n; idxScore++)
        {
            if (score[idxScore] > 0)
            {
                output = "Yes";
            }
            else
            {
                output = "No";
            }
            Console.WriteLine(output);
        }
    }
}