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 C (GCC 5.4.1) (judge verdict: Accepted)

#include <stdio.h>

int main(void)
{
    // N:人数, K:開始時のポイント, Q:正解が出た回数, i番目に正解したのは参加者Ai
    // 正解した人以外のN-1人のポイントが1減る
    // 終了時にポイントが0以下の参加者は敗退する
    int N, K, Q, A[100000], P[100000], i, j, s; // P:参加者のポイント

    scanf("%d %d %d", &N, &K, &Q);

    for(i=0; i<Q; i++){
	scanf("%d", &A[i]);
    }

    for(j=0; j<N; j++){
	P[j] = K; // ポイントを初期化
	P[j] -= Q; // 正解が出た回数だけ全員のポイントを減らす
    }

    for(i=0; i<Q; i++){
	s = A[i]-1; // 正解した人の番号をsに代入
	P[s]++; // 正解した人のポイントを1増やす
    }

    for(j=0; j<N; j++){
	if(P[j] > 0){
	    printf("Yes\n");
	}

	else{
	    printf("No\n");
	}
    }

    return 0;
}