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 Kotlin (1.0.0) (judge verdict: Accepted)

fun main(args: Array<String>) {


    val (n, k, q) = readLine()!!.split(" ").map(String::toInt)

    val alist = mutableListOf<Int>()
    repeat(q) {
        alist += readLine()!!.toInt()
    }

    println(abc141c(n, k, alist))
}

fun abc141c(n: Int, k: Int, alist: MutableList<Int>): Any? {

    val result = mutableListOf<String>()

    val tmpMap = mutableMapOf<Int, Int>()

    for (hito in alist) {
        val value = tmpMap[hito]
        if (value != null) {
            tmpMap[hito] = value + 1
        } else {
            tmpMap[hito] = 1
        }
    }

    repeat(n) {
        if (k - alist.size + (tmpMap[it + 1] ?: 0) > 0) {
            result += "Yes"
        } else {
            result += "No"
        }
    }

//    repeat(n) {
//        val index = it + 1
//
//        var point = k
//        for (a in alist) {
//
//            if (a != index) {
//                point -=1
//            }
//
//            if (point == 0) {
//                result += "No"
//                break
//            }
//        }
//
//        if (point > 0) {
//            result += "Yes"
//        }

//        if (k - huseikai <= 0) {
//            result += "No"
//        } else {
//            result += "Yes"
//        }
//    }
    return result.joinToString("\r\n")
}