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: Time Limit Exceeded)

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

namespace test01
{
    class Program
    {
        static void Main(string[] args)
        {
            var line = U.GetLineIntParse();
            var N = line[0]; // 参加者
            var K = line[1]; // 最初のポイント
            var Q = line[2]; // 正解数

            List<A> x = new List<A>();
            for (int i = 0; i < N; i++)
            {
                x.Add(new A() { num = i + 1, point = K, seikai = 0 });
            }

            for (int i = 0; i < Q; i++)
            {
                var seikaisya = int.Parse(U.GetLine());
                foreach (var y in x)
                {
                    if (y.num == seikaisya)
                    {
                        y.seikai = y.seikai + 1;
                    }
                }
            }

            foreach (var y in x)
            {
                var p = x.Where(e => e.num != y.num).Sum(e => e.seikai);
                y.point = y.point - p;
                if (y.point <= 0)
                {
                    Console.WriteLine("No");
                }
                else
                {
                    Console.WriteLine("Yes");
                }
            }

         
        }

        class A
        {
            public int num { get; set; }
            public int point { get; set; }
            public int seikai { get; set; }
        }

        class U
        {
            public static string GetLine() { return Console.ReadLine(); }

            public static List<int> GetLineIntParse() { return Console.ReadLine().Split().Select(e => int.Parse(e)).ToList(); }
        }
    }
}