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 Haskell (GHC 7.10.3) (judge verdict: Time Limit Exceeded)

import Data.List
import Control.Monad

make::Int->Int->[Int]
make 0 _ = []
make n k = [k] ++ make (n-1) k

func::[Int]->Int->[Int]
func xs x = map pred (take (x-1) xs) ++ [xs !! (x-1)] ++ map pred (drop x xs)

func2::[Int]->[Int]->[[Int]]
func2 [] _ = []
func2 as ans = [answer] ++ func2 (tail as) answer
    where
        answer = func ans (head as)

func3::[Int]->[String]
func3 xs = map (\x-> if x > 0 then "Yes" else "No") xs

main::IO ()
main = do
    [n,k,q] <- map read . words <$> getLine
    as <- replicateM q readLn :: IO  [Int]
    if k > q then replicateM_ n (putStrLn "Yes") else do
        let ans = make n k
        mapM_ putStrLn $ func3 $ last $ func2 as ans