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::Read;
use std::collections::HashMap;

fn main() {
    let mut buf = String::new();
    std::io::stdin().read_to_string(&mut buf).unwrap();

    let answer = solve(&buf);

    println!("{}", answer);
}

fn solve(input: &str) -> String {
    let mut iterator = input.split_whitespace();

    let n: usize = iterator.next().unwrap().parse().unwrap();
    let k: i64 = iterator.next().unwrap().parse().unwrap();
    let q: i64 = iterator.next().unwrap().parse().unwrap();

    let mut map: HashMap<usize, i64> = HashMap::new();
    for _i in 0..q {
        let a: usize = iterator.next().unwrap().parse().unwrap();
        *map.entry(a).or_insert(0) += 1;
    }

    let mut answer = Vec::with_capacity(n);
    for i in 1..(n + 1) {
        if k - q + *map.get(&i).unwrap_or(&0) > 0 {
            answer.push("Yes");
        } else {
            answer.push("No");
        }
    }

    return answer.join("\n");
}

#[test]
fn test() {
    assert_eq!(
        solve(
            r"6 3 4
3
1
3
2"
        ),
        "No
No
Yes
No
No
No"
    );
    assert_eq!(
        solve(
            r"6 5 4
3
1
3
2"
        ),
        "Yes
Yes
Yes
Yes
Yes
Yes"
    );
    assert_eq!(
        solve(
            r"10 13 15
3
1
4
1
5
9
2
6
5
3
5
8
9
7
9"
        ),
        "No
No
No
No
Yes
No
No
No
Yes
No"
    );
}