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;
using System.Collections;
using System.Collections.Generic;
using System.Linq;

namespace AtCoder
{
    public class MainClass
    {
        public static void Main(string[] args)
        {
            if (args.Length > 0 && args[0] == "debug")
            {
                var inputs = new[] { @"
6 3 4
3
1
3
2
				", @"
6 5 4
3
1
3
2
				", @"
10 13 15
3
1
4
1
5
9
2
6
5
3
5
8
9
7
9
				", @"

				", @"

				" };

                foreach (var str in inputs)
                {
                    var text = str.Trim();
                    if (text.Length == 0) continue;
                    var reader = new System.IO.StringReader(text);
                    Console.SetIn(reader);
                    Main2(args);
                    Console.WriteLine();
                    Console.WriteLine("----------------------------------");
                    Console.WriteLine();
                }
            }
            else
                Main2(args);
        }

        public static void Main2(string[] args)
        {
            checked
            {
                var paramsList = Console.ReadLine().Split(' ').ToList();
                // NKQ
                var N = long.Parse(paramsList[0]);
                var K = long.Parse(paramsList[1]);
                var Q = int.Parse(paramsList[2]);

                var A = EnumerablePlus.Repeat(Q, () =>
                {
                    return long.Parse(Console.ReadLine());
                }).ToList();

                var res = new long[N];
                foreach (var a in A)
                {
                    res[a - 1]++;
                }

                for (int i = 0; i < N; i++)
                {
                    res[i] = K - (Q - res[i]);
                }

                var def = Console.Out;
                var sw = new System.IO.StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false };
                Console.SetOut(sw);
                foreach (var item in res.Select(r => r > 0 ? "Yes" : "No"))
                {
                    Console.WriteLine(item);
                }
                Console.Out.Flush();
                Console.SetOut(def);
            }
        }

    }

    public static class EnumerablePlus
    {
        ///<summary>出力文字列に変換。</summary>
        public static string MkString<T>(this IEnumerable<T> list)
        {
            return list.Aggregate(
                new System.Text.StringBuilder(),
                (a, b) => ((a.Length > 0) ? a.Append(' ') : a).Append(b)
                ).ToString();
        }

        ///<summary>添字付きfor。</summary>
        public static void ForEach<T>(this IEnumerable<T> list, Action<T, int> a)
        {
            int i = 0;
            foreach (var item in list)
            {
                a(item, i);
            }
        }

        ///<summary>指定回数デリゲートを呼び出す。</summary>
        public static IEnumerable<T> Repeat<T>(int n, Func<T> f)
        {
            for (int i = 0; i < n; i++)
            {
                yield return f();
            }
        }
    }

    public static class MathPlus
    {
        ///<summary>約数。順番は不定。</summary>
        public static List<long> Divisor(long n)
        {
            var list = Prime(n).
                GroupBy(id => id).
                Select(pair => new { prime = pair.Key, power = pair.Count() }).
                ToList();

            var result = list.Aggregate(new List<long>(), (left, pair) =>
            {
                var list2 = Enumerable.
                    Range(0, pair.power + 1).
                    Aggregate(new List<long>(), (res, l) =>
                    {
                        var next = res.Count > 0 ? res.Last() * pair.prime : 1L;
                        res.Add(next);
                        return res;
                    });

                if (left.Count == 0) return list2.ToList();

                return list2.
                    SelectMany(l => left.Select(m => l * m)).
                    ToList();
            });

            return result;
        }

        ///<summary>順列の数。</summary>
        public static long Permutation(long n, long r)
            => Factorial(n, r);

        ///<summary>組合せの数。</summary>
        public static long Combination(long n, long r)
        {
            if (r == 0) return 1;

            return Factorial(n, r) / Factorial(r);
        }

        ///<summary>階乗。カウントも指定可能。</summary>
        public static long Factorial(long a, long count = long.MaxValue)
        {
            long res = 1;

            for (long i = 0; a > 0 && i < count; i++)
            {
                checked { res *= a; }
                --a;
            }

            return res;
        }

        ///<summary>素因数分解。昇順。</summary>
        public static List<long> Prime(long a)
        {
            var res = new List<long>();

            for (long b = 2, c = (long)Math.Ceiling(Math.Sqrt(a)); b <= c; ++b)
            {
                while (a % b == 0)
                {
                    res.Add(b);
                    a = a / b;
                }
            }

            return res;
        }

        ///<summary>最小公倍数。</summary>
        public static long Lcm(IEnumerable<long> list)
        {
            return list.Aggregate((a, b) => Lcm(a, b));
        }

        ///<summary>最小公倍数。</summary>
        public static long Lcm(long a, long b)
        {
            return checked(a * b) / Gcd(a, b);
        }

        ///<summary>最大公約数。</summary>
        public static long Gcd(IEnumerable<long> list)
        {
            return list.Aggregate((a, b) => Gcd(a, b));
        }

        ///<summary>最大公約数。</summary>
        public static long Gcd(long a, long b)
        {
            if (a < b)
                Gcd(b, a);

            while (b != 0)
            {
                var rem = a % b;
                a = b;
                b = rem;
            }

            return a;
        }

        ///<summary>切り上げ。</summary>
        public static long Ceiling(long a, long b) => (a + (b - 1)) / b;
    }
}