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;
use std::collections::HashMap;

fn read_line() -> String {
    let mut line = String::new();

    io::stdin().read_line(&mut line)
        .expect("Failed to read line");
    return line;
}
fn to_i(s: &str) -> i64 {
    return s.trim().parse()
        .expect("Please type a number!");
}
fn read_nums() -> Vec<i64>
{
    let line = read_line();
    let items: Vec<&str> = line.split(' ').collect();

    let mut nums: Vec<i64> = Vec::new();

    for item in items {
        nums.push(to_i(item));
    }
    return nums;
}


fn main() {
    //println!("start");
    let nkq = read_nums();
    let n = nkq[0];
    let k = nkq[1];
    let q = nkq[2];

    let mut aa = Vec::<i64>::with_capacity(n as usize);
    for i in 0..n {
        aa.push(0);
    }

    for i in 0..q {
        let ai = read_nums()[0] -1;
        aa[ai as usize] += 1;
    }

    for i in 0..n {
        if k-q+aa[i as usize]>0 {
            println!("Yes");
        } else {
            println!("No");
        }
    }


    
    
    
    
}