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::{self, Write};
use io_ext::Reader;
use parse::ParseCollect;

fn main() {
    let stdin = io::stdin();
    let mut r = Reader::new(stdin.lock());
    let (n, k, q): (usize, isize, isize) = r.read_line().split_whitespace().parse_collect();

    let mut pts = vec![0; n];
    for _ in 0..q {
        let ans = r.read_line().parse::<usize>().unwrap() - 1;
        pts[ans] += 1;
    }

    let stdout = io::stdout();
    let mut w = stdout.lock();
    for pt in pts {
        if k + pt - q > 0 {
            writeln!(w, "Yes").unwrap();
        } else {
            writeln!(w, "No").unwrap();
        }
    }
}

/// Extension of io module.
pub mod io_ext {
    use std::mem;
    use std::io::BufRead;

    pub struct Reader<R> {
        buf: String,
        inner: R,
    }

    impl<R> Reader<R> {
        #[inline]
        pub fn new(inner: R) -> Self {
            Reader { buf: String::new(), inner: inner }
        }

        #[inline]
        pub fn into_inner(self) -> R {
            self.inner
        }
    }

    impl<R: BufRead> Reader<R> {
        #[allow(deprecated)]
        #[inline]
        pub fn read_line(&mut self) -> &str {
            self.buf.clear();
            self.inner.read_line(&mut self.buf).unwrap_or_else(|e| panic!("{}", e));
            self.buf.trim_right()
        }

        pub fn read_lines(&mut self, n: usize) -> Lines<R> {
            Lines { reader: self, n: n }
        }
    }

    pub struct Lines<'a, R: 'a> {
        reader: &'a mut Reader<R>,
        n: usize,
    }

    impl<'a, R: BufRead> Iterator for Lines<'a, R> {
        type Item = &'a str;

        fn next(&mut self) -> Option<&'a str> {
            if self.n > 0 {
                self.n -= 1;
                unsafe { Some(mem::transmute::<_, &'a str>(self.reader.read_line())) }
            } else {
                None
            }
        }
    }
}

/// Module supporting to parse strings.
pub mod parse {
    use std::str::FromStr;
    use std::borrow::Borrow;
    use std::collections::BinaryHeap;

    pub trait FromStrIter {
        fn from_str_iter<S: Borrow<str>, I: Iterator<Item=S>>(i: I) -> Self;
    }

    pub trait ParseCollect {
        fn parse_collect<F: FromStrIter>(self) -> F;
    }

    impl<S, I> ParseCollect for I where S: Borrow<str>, I: Iterator<Item=S>
    {
        #[inline]
        fn parse_collect<F: FromStrIter>(self) -> F {
            F::from_str_iter(self)
        }
    }

    fn parse<S: Borrow<str>, I: Iterator<Item=S>, F: FromStr>(i: &mut I) -> F {
        i.next().unwrap_or_else(|| panic!("too few strings error")).borrow().parse().unwrap_or_else(|_| panic!("parse error"))
    }

    impl<A: FromStr, B: FromStr> FromStrIter for (A, B) {
        fn from_str_iter<S: Borrow<str>, I: Iterator<Item=S>>(mut i: I) -> Self {
            let a = parse(&mut i);
            let b = parse(&mut i);
            if i.next().is_some() {
                panic!("too many strings error");
            }
            (a, b)
        }
    }

    impl<A: FromStr, B: FromStr, C: FromStr> FromStrIter for (A, B, C) {
        fn from_str_iter<S: Borrow<str>, I: Iterator<Item=S>>(mut i: I) -> Self {
            let a = parse(&mut i);
            let b = parse(&mut i);
            let c = parse(&mut i);
            if i.next().is_some() {
                panic!("too many strings error");
            }
            (a, b, c)
        }
    }

    impl<T: FromStr> FromStrIter for Vec<T> {
        fn from_str_iter<S: Borrow<str>, I: Iterator<Item=S>>(i: I) -> Self {
            i.map(|s| s.borrow().parse().unwrap_or_else(|_| panic!("parse error"))).collect()
        }
    }

    impl<T: FromStr + Ord> FromStrIter for BinaryHeap<T> {
        fn from_str_iter<S: Borrow<str>, I: Iterator<Item=S>>(i: I) -> Self {
            i.map(|s| s.borrow().parse().unwrap_or_else(|_| panic!("parse error"))).collect()
        }
    }
}