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 Python (3.4.3) (judge verdict: Time Limit Exceeded)

#入力。参加者数N, 初期得点K ,正解数Q
N, K, Q = list(map(int,input().split()))
#入力。正解した人の番号A[i]
A = [None for _ in range(Q)]
for i in range(Q):
  A[i] = int(input())
#初期得点(hp)をリスト化。
hp = [K for _ in range(N)]
#まず他の人への攻撃力at(各人の正解数)を記録。
at = [0 for _ in range(N)]
#正解した人の攻撃力+1。
for i in range(Q):
  j = A[i]
  at[j-1] += 1
#攻撃力分の数を一度全員のhpからマイナスする。
for i in range(N):
  hp[i] -= sum(at)
#各々自分の攻撃力分は本来受けないはずのダメージなのでhpに戻す(足す)。
for i in range(N):
  hp[i] += at[i]
#結果(生き残り判定)
for i in range(N):
  if hp[i] > 0:
    print('Yes')
  else:
    print('No')