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>
using namespace std;

typedef long long ll;
#define REP(i, n, m) for(int i = n; i < m; i++)
#define REPR(i, n, m) for(int i = n; i >= m; i--)
#define LREP(i, n, m) for(ll i = n; i < m; i++)
#define LREPR(i, n, m) for(ll i = n; i >= m; i--)

#define P pair<int, int >


const int INF = 1e9 + 1;
const int MOD = 1e9 + 7;



//---functions---//
int gcd(int a, int b){
    if(a < b) swap(a, b);
    return b?gcd(b, a%b):a;
}

int s2i(string num){stringstream ss; ss << num << flush; int n; ss >> n; return n;}
string i2s(int n){stringstream ss; ss << n << flush; return ss.str();}

bool firstCompare(const P& firstElof, const P& secondElof){
    return firstElof.first < secondElof.first;
}
bool secondCompare(const P& firstElof, const P& secondElof){
    return firstElof.second < secondElof.second;
}
//---------------//
//-----class-----//
class UnionFind{
    public:
        vector<ll> par; //parents
        vector<ll> siz; // sizes of set
        vector<ll> rank; // rank of each element 
    UnionFind(ll n): par(n), siz(n, 1LL), rank(n){
        LREP(i, 0, n) par[i] = i;
    }
    //initialization
    /*
    void init(ll n){
        par.assign(n);
        siz.assign(n, 1LL);
        rank.assign(n);
        LREP(i, 0, n) par[i] = i;
    }
    */

    // find the root of x
    ll find(ll x){
        if(par[x] == x) return x;
        else return par[x] = find(par[x]);
    }

    //Unite two set including x or y
    void unite(ll x, ll y){
        x = find(x);
        y = find(y);
        if(x == y) return;
        if(rank[x] < rank[y]){
            par[x] = y;
            siz[y] += siz[x];
        }else{
            par[y] = x;
            siz[x] += siz[y];
            if(rank[x] == rank[y]) rank[x]++;
        }
    }

    //Do x and y belong to the same set?
    bool issame(ll x, ll y){
        return find(x) == find(y);
    }

};

int N, K, Q;

int main(){
    cin.tie(0);
    cout.tie(0);
    ios::sync_with_stdio(false);
    cin >> N >> K >> Q;
    int points[N];
    REP(i, 0, N) points[i] = K - Q;

    REP(i, 0, Q){
        int A;
        cin >> A;
        --A;
        ++points[A]; 
    }
    REP(i, 0, N){
        if(points[i] > 0) cout << "Yes" << '\n';
        else cout << "No" << '\n';
    }
}