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 Perl (v5.18.2) (judge verdict: Accepted)

use strict;
use warnings;

sub main {
    chomp(my $nkq = <STDIN>);
    my ($N,$K,$Q) = split(/ /,$nkq);
    my @A;
    while(<STDIN>){
        chomp;
        push(@A,$_)
    }
    print solver($N,$K,$Q,\@A);
}
main() unless caller;

sub solver {
    my ($N,$K,$Q,$A) = @_;
    my @ans;
    my $n = $K - $Q;
    my %tmp;
    my %mem;
    if($n>0){
        @ans = map{$_='Yes'}(0..$N-1);
        return join("\n", @ans) . "\n";
    } else {
        for my $i(@$A) {
            $i--;
            unless (defined $mem{$i}) {
                $tmp{$i} = $n;
                $mem{$i} = 1;
            }
            $tmp{$i}++;
        }
    }
    for my $j(0..$N-1) {
        if(defined $tmp{$j} && $tmp{$j} > 0){
            $ans[$j] = 'Yes';
        } else {
            $ans[$j] = 'No';
        }
    }
    return join("\n", @ans) . "\n";
}