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 <algorithm>
#include <iomanip>
#include <iostream>
#include <vector>
using namespace std;
template <class T>
inline bool chmax(T &a, T b) {
  if (a < b) {
    a = b;
    return 1;
  }
  return 0;
}

typedef long long ll;
ll MOD = 1000000007;

// a^p
// 2^3 = 2 * 2^2
// 2^2 = 2 * (2^1)
// 2^1 = 2
ll modpow(ll a, ll p, ll mod) {
  if (p == 0) return 1;

  if (p % 2 == 0) {
    ll half = modpow(a, p / 2, mod) % mod;
    return half * half % mod;
  } else {
    return a * modpow(a, p - 1, mod) % mod;
  }
}

// nCa を求める
ll modCombination(ll n, ll a, ll mod) {
  if (n - a < a) {
    return modCombination(n, n - a, mod);
  }

  ll denominator = 1;  // 分母
  ll numerator = 1;    // 分子

  for (ll i = 0; i < a; i++) {
    denominator *= a - i;
    numerator *= n - i;
    denominator %= mod;
    numerator %= mod;
  }

  return numerator * modpow(denominator, mod - 2, mod) % mod;
}

class UnionFind {
 private:
  vector<ll> parents;

 public:
  UnionFind(ll n) : parents(n, -1) {}

  bool issame(ll x, ll y) { return root(x) == root(y); }

  bool merge(ll x, ll y) {
    if (issame(x, y)) return false;

    ll rx = root(x);
    ll ry = root(y);
    if (parents[rx] > parents[ry]) swap(rx, ry);
    // サイズ情報を更新
    parents[rx] += parents[ry];
    // yの親を更新
    parents[ry] = rx;

    return true;
  }

  ll size(ll x) { return -parents[root(x)]; }

 private:
  ll root(ll x) {
    if (parents[x] < 0) return x;
    // 根の親の値に木の(-)サイズの情報を入れる
    return parents[x] = root(parents[x]);
  }
};

ll gcd(ll a, ll b) {
  if (a % b == 0) {
    return (b);
  } else {
    return (gcd(b, a % b));
  }
}

int main() {
  cin.tie(nullptr);
  ios_base::sync_with_stdio(false);
  cout << fixed << setprecision(15);

  ll N, K, Q;
  cin >> N >> K >> Q;
  vector<ll> A(N, 0);
  for (ll i = 0; i < Q; i++) {
    ll a;
    cin >> a;
    A[a - 1]++;
  }
  ll n = Q - K + 1;

  if (n <= 0) {
    for (ll i = 0; i < N; i++) {
      cout << "Yes" << endl;
    }
  } else {
    for (ll i = 0; i < N; i++) {
      if (A[i] >= n) {
        cout << "Yes" << endl;
      } else {
        cout << "No" << endl;
      }
    }
  }

  return 0;
}