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)

#if true
//#if false
#define UTAKA_DEBUG
#endif

using System;
using System.Collections;
using System.Collections.Generic;
using System.Diagnostics.CodeAnalysis;
using System.IO;
using System.Linq;
using System.Net.Mime;
using System.Text;

namespace UtakaApp
{
    public partial class Program
    {
        public const string ContestName = "abc141";
        public const string ProblemName = "C";

        public static void Main(string[] args)
        {
#if UTAKA_LOCAL
//#if false
            new TestCaseCheckerForAtCoder().TestProblems();
#else
            var console = new MyConsole();
            new Program().Solve(System.Console.In, console);
            console.Flush();
#endif
            var sw = new StreamWriter(Console.OpenStandardOutput()) {AutoFlush = false};
        }

        public void Solve(TextReader textReader, IConsole console)
        {
            var cin = new ConsoleInput(textReader);

            int N = cin.ReadInt;
            int K = cin.ReadInt;
            int Q = cin.ReadInt;

            int[] A = new int[Q];

            for (int i = 0; i < Q; i++)
            {
                A[i] = cin.ReadInt;
            }
            
            int[] okCounts = new int[N];

            for (int i = 0; i < A.Length; i++)
            {
                var index = A[i] - 1;
                okCounts[index]++;
            }

            for (int j = 0; j < N; j++)
            {
                int score = K - Q + okCounts[j];
                
                console.WriteLine(score > 0 ? "Yes" : "No");
            }
        }
    }

    public partial class Program
    {
        public const int ModLarge = 1000000007;
    }

    public class ConsoleInput
    {
        private readonly TextReader _stream;
        private readonly char _separator = ' ';
        private readonly Queue<string> inputStream;

        public ConsoleInput(TextReader stream, char separator = ' ')
        {
            _separator = separator;
            _stream = stream;
            inputStream = new Queue<string>();
        }

        public string Read
        {
            get
            {
                if (inputStream.Count != 0)
                {
                    return inputStream.Dequeue();
                }

                var tmp = _stream.ReadLine().Split(_separator);
                for (var i = 0; i < tmp.Length; ++i)
                {
                    inputStream.Enqueue(tmp[i]);
                }

                return inputStream.Dequeue();
            }
        }

        public string ReadLine => _stream.ReadLine();
        public int ReadInt => int.Parse(Read);
        public long ReadLong => long.Parse(Read);
        public double ReadDouble => double.Parse(Read);

        public string[] ReadStrArray(long N)
        {
            var ret = new string[N];
            for (long i = 0; i < N; ++i)
            {
                ret[i] = Read;
            }

            return ret;
        }

        public int[] ReadIntArray(long N)
        {
            var ret = new int[N];
            for (long i = 0; i < N; ++i)
            {
                ret[i] = ReadInt;
            }

            return ret;
        }

        public long[] ReadLongArray(long N)
        {
            var ret = new long[N];
            for (long i = 0; i < N; ++i)
            {
                ret[i] = ReadLong;
            }

            return ret;
        }
    }

    public interface IConsole
    {
        void Flush();
        void Write(string str);
        void WriteLine(string str);
    }

    public class MyConsole : IConsole
    {
        public MyConsole()
        {
            var sw = new StreamWriter(Console.OpenStandardOutput()) {AutoFlush = false};
            Console.SetOut(sw);
        }

        public void Flush()
        {
            Console.Out.Flush();
        }

        public void Write(string str)
        {
            Console.Write(str);
        }

        public void WriteLine(string str)
        {
            Console.WriteLine(str);
        }
    }

#if UTAKA_LOCAL

    public class DebugConsole : IConsole
    {
        private readonly StringBuilder mSb;

        public DebugConsole()
        {
            mSb = new StringBuilder();
        }

        public void Flush()
        {
            // 何もしない
        }

        public void Write(string str)
        {
            mSb.Append(str);
        }

        public void WriteLine(string str)
        {
            mSb.AppendLine(str);
        }

        public string GetAllOutput()
        {
            return mSb.ToString();
        }
    }

#endif

#if UTAKA_LOCAL

    public class TestCaseCheckerForAtCoder
    {
        private string DirectoryPath => $"../../../../{Program.ContestName}/{Program.ProblemName}";

        private string GetInputFilePath(int testCaseNumber)
        {
            //return $"{DirectoryPath}/sample-{testCaseNumber}.in";
            return $"{DirectoryPath}/in_{testCaseNumber}.txt";
        }

        private string GetOutputFilePath(int testCaseNumber)
        {
            //return $"{DirectoryPath}/sample-{testCaseNumber}.out";
            return $"{DirectoryPath}/out_{testCaseNumber}.txt";
        }

        public bool TestProblem(int testCaseNumber)
        {
            var inputFilePath = GetInputFilePath(testCaseNumber);
            var outputFilePath = GetOutputFilePath(testCaseNumber);

            TextReader inputStream = new StreamReader(inputFilePath);

            var debugConsoleWriter = new DebugConsole();

            new Program().Solve(inputStream, debugConsoleWriter);

            var output = debugConsoleWriter.GetAllOutput();

            TextReader outputStream = new StreamReader(outputFilePath);
            var outputAnswer = outputStream.ReadToEnd();

            Dbg.WriteLine(output);
            Dbg.WriteLine(outputAnswer);

            var isCorrect = output == outputAnswer;

            return isCorrect;
        }

        public void TestProblems()
        {
            var isSuccessAll = true;

            var testCaseNumber = 1;
            while (true)
            {
                var inputFileName = GetInputFilePath(testCaseNumber);
                if (!File.Exists(inputFileName))
                {
                    break;
                }

                Console.WriteLine($"TestCase {testCaseNumber} =====================================================");

                var result = TestProblem(testCaseNumber);

                if (result)
                {
                    Console.WriteLine("Success");
                }
                else
                {
                    isSuccessAll = false;
                    Console.WriteLine("Failure *****");
                }

                testCaseNumber++;
            }

            if (isSuccessAll)
            {
                Console.WriteLine("!!!!!!!!! All Success !!!!!!!!!");
            }
        }
    }

#endif

#if UTAKA_LOCAL

    public static class Dbg
    {
        public static void WriteLine(string str)
        {
            Console.WriteLine(str);
        }

        public static void Write(string str)
        {
            Console.Write(str);
        }
    }
#else
    public static class Dbg
    {
        public static void WriteLine(string str)
        {
        }

        public static void Write(string str)
        {
        }
    }

#endif
}