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(dead_code)]
#![allow(non_snake_case)]
// Original macro is in https://qiita.com/tanakh/items/0ba42c7ca36cd29d0ac8
// Thanks @tanakh :bow:
macro_rules! input {
    ($($r:tt)*) => {
        let stdin = std::io::stdin();
        let mut bytes = std::io::Read::bytes(std::io::BufReader::new(stdin.lock()));
        let mut next = || -> String {
            bytes
                .by_ref()
                .map(|r|r.unwrap() as char)
                .skip_while(|c|c.is_whitespace())
                .take_while(|c|!c.is_whitespace())
                .collect()
        };
        input_inner!{next, $($r)*}
    };
}
 
macro_rules! input_inner {
    ($next:expr) => {};
    ($next:expr, ) => {};
 
    ($next:expr, $var:ident : $t:tt $($r:tt)*) => {
        let $var = read_value!($next, $t);
        input_inner!{$next $($r)*}
    };
    
    ($next:expr, mut $var:ident : $t:tt $($r:tt)*) => {
        let mut $var = read_value!($next, $t);
        input_inner!{$next $($r)*}
    };
}
 
macro_rules! read_value {
    ($next:expr, ( $($t:tt),* )) => {
        ( $(read_value!($next, $t)),* )
    };
 
    ($next:expr, [ $t:tt ; $len:expr ]) => {
        (0..$len).map(|_| read_value!($next, $t)).collect::<Vec<_>>()
    };

    ($next:expr, [$t:tt]) => {
        {
            let len = read_value!($next, usize);
            (0..len).map(|_| read_value!($next, $t)).collect::<Vec<_>>()
        }
    };
 
    ($next:expr, chars) => {
        read_value!($next, String).chars().collect::<Vec<char>>()
    };
 
    ($next:expr, usize1) => {
        read_value!($next, usize) - 1
    };
 
    ($next:expr, $t:ty) => {
        $next().parse::<$t>().expect("Parse error")
    };
}

// for adhoc read (ex. https://atcoder.jp/contests/abc112/tasks/abc112_a)
fn read_line() -> String {
    let mut s = String::new();
    std::io::stdin().read_line(&mut s).unwrap();
    s.trim().to_string()
}

#[derive(Debug)]
struct Matrix<T=f32> {
    row: usize,
    col: usize,
    matrix: Vec<Vec<T>>,
}

impl Matrix {
    fn rank(&mut self) -> usize {
        let mut rank = 0;

        for col in 0..self.col {
            let mut pivot = 1000000;
            let mut ma = 1e-10;
            for row in rank..self.row {
                if self.matrix[row][col].abs() > ma {
                    ma = self.matrix[row][col].abs();
                    pivot = row;
                }
            }
            if pivot == 1000000 {
                continue;
            }
            self.matrix.swap(pivot, rank);

            let div = self.matrix[rank][col];
            for col2 in 0..self.col { self.matrix[rank][col2] /= div; }
            for row in 0..self.row {
                if row != rank && self.matrix[row][col].abs() > 1e-10 {
                    let fac = self.matrix[row][col];
                    for col2 in 0..self.col {
                        self.matrix[row][col2] -= self.matrix[rank][col2] * fac;
                    }
                }
            }
            rank += 1;
            // println!("---------------------");
            // println!("col {}", col);
            // println!("pivot {}, rank {}", pivot, rank);
            // println!("  swapped matrix {:?}", self.matrix);
        }
        return rank;
    }
}
// https://practice.contest.atcoder.jp/tasks/practice_1
fn main() {
    input! {
        N: usize, K: i32, Q: i32,
        a: [usize; Q]
    }
    let mut b = vec![0;N];
    for answer in a {
        b[answer-1] += 1;
    }
    // println!("{:?}", b);
    for i in 0..N {
        if K - Q + b[i] <= 0 {
            println!("{}", "No");
        } else {
            println!("{}", "Yes");
        }
    }
}