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 Rust (1.15.1) (judge verdict: Accepted)

use std::io::{self, BufRead, Write};

fn solve<R, W>(reader: R, mut writer: W)
where
    R: BufRead,
    W: Write,
{
    let mut lines = reader.lines();
    let a_line = lines.next().unwrap().unwrap();
    let mut splited = a_line.trim().split_whitespace();
    let n: usize = splited.next().unwrap().parse().unwrap();
    let k: i32 = splited.next().unwrap().parse().unwrap();
    let q: i32 = splited.next().unwrap().parse().unwrap();

    let mut points = vec![0; n];
    for l in lines {
        let answered_plus_one: i32 = l.unwrap().trim().parse().unwrap();
        points[(answered_plus_one - 1) as usize] += 1;
    }

    for p in points {
        let ans = if k - q + p > 0 {
            "Yes"
        } else {
            "No"
        };
        writeln!(&mut writer, "{}", ans).unwrap();
    }
}

fn main() {
    let stdio = io::stdin();
    let input = stdio.lock();

    let output = io::stdout();

    solve(input, output);
}

#[cfg(test)]
mod tests {
    use super::*;

    const TESTS: &'static [(&'static [u8], &'static [u8])] = &[
        (
            br"6 3 4
3
1
3
2", br"No
No
Yes
No
No
No
",
        ),
        (
            br"6 5 4
3
1
3
2", br"Yes
Yes
Yes
Yes
Yes
Yes
",
        ),
        (
            br"10 13 15
3
1
4
1
5
9
2
6
5
3
5
8
9
7
9", br"No
No
No
No
Yes
No
No
No
Yes
No
",
        ),
    ];

    #[test]
    fn test_c() {
        for &(input, expected) in TESTS {
            let mut output = Vec::new();
            solve(input, &mut output);
            let expected_str = String::from_utf8(expected.to_vec()).unwrap();
            let output_str = String::from_utf8(output).unwrap();
            assert_eq!(expected_str, output_str);
        }
    }
}