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)

#![allow(unused_imports)]
#![allow(unused_macros)]
#![allow(dead_code)]
#![allow(non_snake_case)]

use std::collections::{BinaryHeap,HashMap,HashSet};
use std::fmt::Debug;
use std::io::stdin;
use std::str::FromStr;
use std::borrow::Borrow;

/*
i32 = 10^9 (-2147483648 < x < 2147483647)
i64 = 10^18 (-9223372036854775808 < x < 9223372036854775807)
u32 = 10^9 (0 < x < 4294967295)
u64 = 10^19 (0 < x < 18446744073709551615)
*/

macro_rules! read {
  ($($t: ty),+) => ({
    let mut input = String::new();
    stdin().read_line(&mut input).expect("read error");
    let mut iter = input.split_whitespace();
    ($(iter.next().unwrap().parse::<$t>().expect("parse error"),)+)
  })
}

macro_rules! puts {
  ($($t:expr),+) => {
    $(print!("{} ", &$t);)+
    print!("\n");
  }
}

macro_rules! entry {
  ($map:expr, $idx:expr) => {(*$map.entry($idx).or_insert(0))}
}

fn main() {
  let (N, K, Q) = read!(i32, i32, i32);

  let mut score = HashMap::<i32, i32>::new();
  for _ in 0..Q {
    entry!(score, read::<i32>() - 1) += 1;
  }
  
  for i in 0..N {
    if K - (Q - entry!(score, i)) > 0 {
      print("Yes");
    } else {
      print("No");
    }
  }
}

fn print<T: std::fmt::Display>(target: T)  {
  println!("{}", target);
}

fn debug<T: Debug>(target: &T) {
  println!("{:?}", target);
}

// read from stdin
fn read<T: FromStr>() -> T {
  let mut s = String::new();
  stdin().read_line(&mut s).ok();
  s.trim().parse().ok().unwrap()
}

// read from stdin as whitespace separated vector
fn read_hvec<T: FromStr>() -> Vec<T> {
  let mut s = String::new();
  stdin().read_line(&mut s).ok();
  s.trim()
    .split_whitespace()
    .map(|e| e.parse().ok().unwrap())
    .collect()
}

// read from stdin as line separated vector
fn read_vseq<T: FromStr>(n: u64) -> Vec<T> {
  let mut v = Vec::new();
  for _ in 0..n {
    let mut text = String::new();
    stdin().read_line(&mut text).ok();
    let parsed = text.trim().parse().ok().unwrap();
    v.push(parsed);
  }
  v
}

fn read_matrix<T: FromStr>(n: u32) -> Vec<Vec<T>> {
  let mut v2 = Vec::new();
  for _ in 0..n {
    let mut s = String::new();
    stdin().read_line(&mut s).ok();
    let v = s
      .trim()
      .split_whitespace()
      .map(|e| e.parse().ok().unwrap())
      .collect();
    v2.push(v);
  }
  v2
}