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.Linq;
using System.Collections.Generic;

namespace Contest
{
    class Program
    {
        static void Main(string[] args)
        {
            ABC141.C();
        }

        class ABC141
        {
            public static void A()
            {
                var S = Read.Str();
                var weather = new string[] { "Sunny", "Cloudy", "Rainy" };
                Console.WriteLine(weather[(weather.ToList().IndexOf(S) + 1) % 3]);
            }
            public static void B()
            {
                var S = Read.Str();
                for (int i = 0; i < S.Length; ++i)
                {
                    if (S[i] == (i % 2 == 0 ? 'L' : 'R'))
                    {
                        Console.WriteLine("No"); return;
                    }
                }
                Console.WriteLine("Yes");
            }
            public static void C()
            {
                var N = Read.Int();
                var K = Read.Int();
                var Q = Read.Int();
                var A = Enumerable.Range(0, Q).Select(i => Read.Int());
                var point = Enumerable.Range(0, N).Select(i => K - Q).ToArray();
                foreach(var a in A)
                {
                    point[a - 1]++;
                }
                var sb = new System.Text.StringBuilder();
                foreach(var p in point)
                {
                    sb.AppendLine(p > 0 ? "Yes" : "No");
                }
                Console.Write(sb.ToString());
            }
            public static void D()
            {
                var N = Read.Int();
                var M = Read.Int();
                var A = Read.LongN();
                var queue = new Util.PriorityQueue<long>(N, false);
                foreach(var a in A)
                {
                    queue.Push(a);
                }
                for(int i = 0; i < M; ++i)
                {
                    var v = queue.Pop();
                    queue.Push(v / 2);
                }
                long sum = 0;
                while (queue.Count() > 0)
                {
                    sum += queue.Pop();
                }
                Console.WriteLine(sum);
            }
            public static void E()
            {
                var N = Read.Int();
                var S = Read.Str();
                int max = 0;
                for(int i = 0; i < N -2; ++i)
                {
                    var Z = Util.ZAlgorithm(S.Substring(i));
                    for(int j = 0; j < Z.Length; ++j)
                    {
                        max = Math.Max(max, Math.Min(j, Z[j]));
                    }
                }
                Console.WriteLine(max);
            }
            public static void F()
            {

            }
        }

        class Util
        {
            public class PriorityQueue<T> where T : IComparable
            {
                private IComparer<T> _comparer = null; private bool _isAsc = true; private T[] _heap; private int _sz = 0;
                public PriorityQueue(int maxSize, IComparer<T> comparer) { _heap = new T[maxSize]; _comparer = comparer; }
                public PriorityQueue(int maxSize, bool isAsc = true) { _heap = new T[maxSize]; _isAsc = isAsc; }
                private int Compare(T x, T y) { if (_comparer != null) { return _comparer.Compare(x, y); } return _isAsc ? x.CompareTo(y) : y.CompareTo(x); }
                public void Push(T x) { var i = _sz++; while (i > 0) { var p = (i - 1) / 2; if (Compare(_heap[p], x) <= 0) { break; } _heap[i] = _heap[p]; i = p; } _heap[i] = x; }
                public T Pop() { T ret = _heap[0]; T x = _heap[--_sz]; int i = 0; while (i * 2 + 1 < _sz) { int a = i * 2 + 1; int b = i * 2 + 2; if (b < _sz && Compare(_heap[b], _heap[a]) < 0) { a = b; } if (Compare(_heap[a], x) >= 0) { break; } _heap[i] = _heap[a]; i = a; } _heap[i] = x; return ret; }
                public int Count() { return _sz; }
                public T Peek() { return _heap[0]; }
                public bool Contains(T x) { for (int i = 0; i < _sz; i++) if (x.Equals(_heap[i])) return true; return false; }
            }
            public static int[] ZAlgorithm(string S)
            {
                var N = S.Length;
                var Z = new int[N];
                Z[0] = N;
                int i = 1, j = 0;
                while (i < N)
                {
                    while (i + j < N && S[i + j] == S[j]) { j++; }
                    Z[i] = j;
                    if (j == 0) { i++; continue; }
                    int k = 1;
                    while (k < j && k + Z[k] < j) { Z[i + k] = Z[k]; k++; }
                    i += k;j -= k;
                }
                return Z;
            }
        }

        static class Read
        {
            static Queue<string> queue = new Queue<string>();
            static void Enqueue() { var ss = Console.ReadLine().Split(' '); foreach (var s in ss) { queue.Enqueue(s); } }
            public static int Int() { if (queue.Count == 0) { Enqueue(); } return Convert.ToInt32(queue.Dequeue()); }
            public static long Long() { if (queue.Count == 0) { Enqueue(); } return Convert.ToInt64(queue.Dequeue()); }
            public static string Str() { if (queue.Count == 0) { Enqueue(); } return queue.Dequeue(); }
            public static int[] IntN() { return Console.ReadLine().Split(' ').Select(s => Convert.ToInt32(s)).ToArray(); }
            public static long[] LongN() { return Console.ReadLine().Split(' ').Select(s => Convert.ToInt64(s)).ToArray(); }
            public static string[] StrN() { return Console.ReadLine().Split(' '); }
            public static Tuple<int, int>[] TupleInt(int n) { List<Tuple<int, int>> list = new List<Tuple<int, int>>(); for (int i = 0; i < n; ++i) { var ab = Read.IntN(); list.Add(new Tuple<int, int>(ab[0], ab[1])); } return list.ToArray(); }
            public static Tuple<long, long>[] TupleLong(int n) { List<Tuple<long, long>> list = new List<Tuple<long, long>>(); for (int i = 0; i < n; ++i) { var ab = Read.LongN(); list.Add(new Tuple<long, long>(ab[0], ab[1])); } return list.ToArray(); }
            public static Tuple<string, string>[] TupleStr(int n) { List<Tuple<string, string>> list = new List<Tuple<string, string>>(); for (int i = 0; i < n; ++i) { var ab = Read.StrN(); list.Add(new Tuple<string, string>(ab[0], ab[1])); } return list.ToArray(); }
            public static Tuple<double, double>[] TupleDouble(int n) { List<Tuple<double, double>> list = new List<Tuple<double, double>>(); for (int i = 0; i < n; ++i) { var ab = Read.LongN(); list.Add(new Tuple<double, double>(ab[0], ab[1])); } return list.ToArray(); }
            public static long[,] LongMatrix(int r, int c)
            {
                var mat = new long[r, c];
                for (int i = 0; i < r; ++i)
                {
                    var x = Read.LongN();
                    for (int j = 0; j < c; ++j)
                    {
                        mat[i, j] = x[j];
                    }
                }
                return mat;
            }
            public static Dictionary<int, HashSet<int>> AdjacencyList(int N, int M, bool isDirectional = false)
            {
                Dictionary<int, HashSet<int>> dict = new Dictionary<int, HashSet<int>>();
                for (int i = 0; i <= N; ++i) { dict.Add(i, new HashSet<int>()); }
                for (int i = 0; i < M; ++i)
                {
                    var ab = Read.IntN(); dict[ab[0]].Add(ab[1]);
                    if (!isDirectional) { dict[ab[1]].Add(ab[0]); }
                }
                return dict;
            }
            public static Dictionary<int, Dictionary<int, long>> AdjacencyListWithWeight(int N, int M)
            {
                Dictionary<int, Dictionary<int, long>> dict = new Dictionary<int, Dictionary<int, long>>();
                for (int i = 0; i <= N; ++i)
                {
                    dict.Add(i, new Dictionary<int, long>());
                }
                for (int i = 0; i < M; ++i)
                {
                    var ab = Read.IntN();
                    dict[ab[0]].Add(ab[1], ab[2]);
                    dict[ab[1]].Add(ab[0], ab[2]);
                }
                return dict;
            }
        }
    }
}