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)

fn input_c() -> std::io::Cursor<String> {
	let mut s = String::new();
	std::io::stdin().read_line(&mut s).unwrap();
	std::io::Cursor::new(s.trim().to_owned())
}
 
fn input_nt<T: std::str::FromStr>(n: usize) -> Vec<T> {
	use std::io::{BufRead, Read};
	let mut v = Vec::with_capacity(n);
	let     i = std::io::stdin();
	let mut l = i.lock();
	let mut r = l.by_ref();
	for _ in 0..n {
		let mut s = String::new();
		r.read_line(&mut s).unwrap();
		v.push(s.trim().parse().ok().unwrap());
	}
	v
}
 
fn read_t<T: std::str::FromStr>(r: &mut std::io::Read) -> T {
	use std::io::Read;
	use std::iter::Iterator;
	r.bytes().map(|b| b.ok().unwrap() as char).skip_while(|c| c.is_whitespace() == true).take_while(|c| c.is_whitespace() == false).collect::<String>().parse().ok().unwrap()
}

fn main() {
	let mut c  = input_c();
    let     n  = read_t::<usize>(&mut c);
    let     k  = read_t::<usize>(&mut c);
    let     q  = read_t::<usize>(&mut c);
    let     xs = input_nt::<usize>(q);
    let mut ys = Vec::with_capacity(n + 1);
    
    ys.resize(n + 1, 0);
    
    for x in &xs {
    	ys[*x] += 1;
    }
    
    for y in &ys[1..(n + 1)] {
    	println!("{}", if 0 < (k as i32) + y - (q as i32) { "Yes" } else { "No" });
    }
}