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++14 (GCC 5.4.1) (judge verdict: Accepted)

#include<cstdio>
#include<algorithm>
#include<vector>
#include<set>
#include<queue>
#define R(i, n) for(int i = 0; i < n; i++)
#define S(a) scanf("%d", &a)
#define S2(a, b) scanf("%d%d", &a, &b)
#define S3(a, b, c) scanf("%d%d%d",  &a, &b, &c)
#define P(a) printf("%d\n", a)
#define INF 1000000000
using namespace std;
typedef long long ll;
typedef pair<int, int> IR;

int N, Q;
ll K;

int main(){
	S(N);
	scanf("%lld", &K);
	S(Q);
	ll must_win;
	if(K > Q){
		R(i, N){
			printf("Yes\n");
		}
		return 0;
	}
	else {must_win = Q - K + 1;
	int ans_num[100001] = {0};
	bool is_clear[100001] = {false};
	R(i, Q){
		int n;
		S(n);
		ans_num[n]++;
		if(ans_num[n] >= must_win) is_clear[n] = true;
	}
	for(int i = 1; i <= N; i++){
		if(is_clear[i]) printf("Yes\n");
		else printf("No\n");
	}
	return 0;}
}