101412: [AtCoder]ABC141 C - Attack Survival

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