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 (Clang 3.8.0) (judge verdict: Accepted)

//Twitter@KonoLv1 2020年春卒で現在就職活動中！
 
#include <stdio.h>
#include <math.h>
#include <string.h>
#include <stdlib.h>
 
int main(void){
    int i,j;            //  ループ文に使用
    int x,y,z,n,k,q;
    int count1,count2,count;   //  カウント用に使用
    int box[100001] = {};
    char s[200001] = {};        //  文字列
    char s2[200001] = {};        //  文字列
    int a,b,c;
    a = b = c = i = 0;
    int mode = 0;
    count = count1 = count2 = 0;
 
    //  入力処理
    
    scanf("%d %d %d",&n,&k,&q);
    for (i = 0; i < q; i++){
        scanf("%d",&x);
        box[x - 1] = box[x - 1] + 1;
    }
 
    //  計算処理
    count1 = k - q;

 //  出力処理

    for (i = 0; i < n; i++){
        box[i] = box[i] + count1;
        if (box[i] > 0){
            printf("Yes\n");
        }else{
            printf("No\n");
        }
    }

}