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 <bits/stdc++.h>
/**  I'm Klaus, NicKlaus :v **/
using namespace std;
#define ms(a,v) memset(a,v,sizeof a)
#define ll long long
#define LOG2(X) ((unsigned) (8*sizeof(int) - __builtin_clz((X)) - 1))
ll gcd(ll x, ll y){return (y ? gcd(y, x%y) : x); }
ll lcm(ll x, ll y){return x*(y/gcd(x,y));}
//~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
int main(){
	ios_base::sync_with_stdio(0), cin.tie(0), cout.tie(0);
	#ifdef LOCAL_JUDGE
		//freopen("in_out/in.txt", "rt", stdin);
		//freopen("int_out/out.txt", "wt", stdout);
	#endif
	int n, k, q;
	cin>>n>>k>>q;
	vector<int> frq(n,0);
	for(int i=0; i<q; i++){
		int x; cin>>x;
		frq[x-1]++;
	}
	int ans = 0;
	for(int i=0; i<n; i++){
		if(k-(q - frq[i]) > 0){
			cout<<"Yes"<<endl;
		}else{
			cout<<"No"<<endl;
		}
	}
	return 0;
}