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 Go (1.6) (judge verdict: Accepted)

package main

import (
	"bufio"
	"fmt"
	basicIO "io"
	"os"
	"strconv"
)

func main() {
	protagonist(os.Stdin, os.Stdout)
}

func protagonist(r basicIO.Reader, w basicIO.Writer) {
	io := NewIO(r, w)
	N, _ := io.nextInt()
	K, _ := io.nextInt()
	Q, _ := io.nextInt()

	A := make([]int, N)

	for i := 0; i < Q; i++ {
		n, _ := io.nextInt()
		A[n-1]++
	}

	for _, val := range A {
		if (Q - val) < K {
			io.PutString("Yes")
		} else {
			io.PutString("No")
		}
	}
}

type IO struct {
	Scanner *bufio.Scanner
	Writer  basicIO.Writer
}

func NewIO(r basicIO.Reader, w basicIO.Writer) *IO {
	s := bufio.NewScanner(r)
	s.Split(bufio.ScanWords)
	return &IO{
		Scanner: s,
		Writer:  w,
	}
}

func (io *IO) nextString() string {
	io.Scanner.Scan()
	return io.Scanner.Text()
}

func (io *IO) nextInt() (int, error) {
	io.Scanner.Scan()
	i, err := strconv.Atoi(io.Scanner.Text())
	return i, err
}

func (io *IO) PutInt(v int) {
	fmt.Fprintf(io.Writer, "%d\n", v)
}

func (io *IO) PutString(s string) {
	fmt.Fprintf(io.Writer, "%s\n", s)
}