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.IO;
using System.Linq;

namespace lineAralgebra
{
	class Program
	{
		static void Main(string[] args)
		{
			var input = Console.ReadLine().Split(' ');
			var n = int.Parse(input[0]);
			var k = int.Parse(input[1]);
			var q = int.Parse(input[2]);

			var users = new int[n];
			for (var i = 0; i < users.Length; i++)
			{
				users[i] = k;
			}

			var a = new int[q];

			for (var i = 0; i < a.Length; i++)
			{
				a[i] = int.Parse(Console.ReadLine());
			}

			for (var i = 0; i < a.Length; i++)
			{
				var correct = a[i] - 1;
				for (var j = 0; j < users.Length; j++)
				{
					if (j == correct) continue;
					users[j]--;
				}
			}
			for (var i = 0; i < users.Length; i++)
			{
				if (users[i] > 0) System.Console.WriteLine("Yes");
				else
				{
					System.Console.WriteLine("No");
				}
			}

		}

		/** test cases:
		 * null ==> null
		 * 1 ==> 1
		 * 1->2 ==> 2->1
		 * 1->2->3 ==> 2->1->3
		 * 1->2->3->4 ==> 2->1->4->3
		 */
	}
}