Problem:
Score : 300 points

Problem Statement

Iroha is very particular about numbers. There are K digits that she dislikes: D_1, D_2, ..., D_K.

She is shopping, and now paying at the cashier.
Her total is N yen (the currency of Japan), thus she has to hand at least N yen to the cashier (and possibly receive the change).

However, as mentioned before, she is very particular about numbers. When she hands money to the cashier, the decimal notation of the amount must not contain any digits that she dislikes. Under this condition, she will hand the minimum amount of money.

Find the amount of money that she will hand to the cashier.

Constraints

1 ≦ N < 10000

1 ≦ K < 10

0 ≦ D_1 < D_2 < … < D_K≦9

\{D_1,D_2,...,D_K\} ≠ \{1,2,3,4,5,6,7,8,9\}

Input

The input is given from Standard Input in the following format:

N K
D_1 D_2 … D_K

Output

Print the amount of money that Iroha will hand to the cashier.

Sample Input 1

1000 8
1 3 4 5 6 7 8 9

Sample Output 1

2000

She dislikes all digits except 0 and 2.

The smallest integer equal to or greater than N=1000 whose decimal notation contains only 0 and 2, is 2000.

Sample Input 2

9999 1
0

Sample Output 2

9999

Solution in C++14 (GCC 5.4.1) (judge verdict: Accepted)

//  Copyright 2020 Nikita Golikov

#include <bits/stdc++.h>

using namespace std;

using i64 = int64_t;
using ui64 = uint64_t;

#ifdef GOLIKOV
mt19937_64 rng(566);
#else
mt19937_64 rng(chrono::steady_clock::now().time_since_epoch().count());
#endif

template <typename T>
T rnd_helper(T from, T to, true_type) {
  return uniform_int_distribution<T>(from, to)(rng);
}

template <typename T>
T rnd_helper(T from, T to, false_type) {
  return uniform_real_distribution<T>(from, to)(rng);
}

template <typename T>
T rnd(T from, T to) {
  return rnd_helper(from, to, is_integral<T>{});
}

template <typename A, typename B, typename Cmp>
bool set_min(A &x, B const &y, Cmp &&cmp) {
  if (cmp(y, x)) {
    x = y;
    return true;
  }
  return false;
}

template <typename A, typename B>
bool set_min(A &x, B const &y) {
  return set_min(x, y, less<typename common_type<A, B>::type>{});
}

template <typename A, typename B>
bool set_max(A &x, B const &y) {
  return set_min(x, y, greater<typename common_type<A, B>::type>{});
}

#include <ext/pb_ds/assoc_container.hpp>

using namespace __gnu_pbds;

template <typename T>
using ordered_set = tree<T, null_type, less<T>, rb_tree_tag,
                         tree_order_statistics_node_update>;

template <typename K, typename V>
using ordered_map = tree<K, V, less<K>, rb_tree_tag,
                         tree_order_statistics_node_update>;

//  https://codeforces.com/blog/entry/62393
struct custom_hash {
  static uint64_t splitmix64(uint64_t x) {
    // http://xorshift.di.unimi.it/splitmix64.c
    x += 0x9e3779b97f4a7c15;
    x = (x ^ (x >> 30)) * 0xbf58476d1ce4e5b9;
    x = (x ^ (x >> 27)) * 0x94d049bb133111eb;
    return x ^ (x >> 31);
  }

  size_t operator()(uint64_t x) const {
    static const uint64_t
        FIXED_RANDOM = chrono::steady_clock::now().time_since_epoch().count();
    return static_cast<size_t>(splitmix64(x + FIXED_RANDOM));
  }
};

#ifdef __cpp_deduction_guides
template <typename F>
struct rec_fun {
  F fun;

  rec_fun(F &&fun_) : fun(std::forward<F>(fun_)) {}

  template <typename... Args>
  decltype(auto) operator()(Args &&... args) const {
    return fun(*this, std::forward<Args>(args)...);
  }
};
#endif

#ifdef __cpp_inline_variables
template <typename T>
inline constexpr auto type_min = numeric_limits<T>::min();

template <typename T>
inline constexpr auto type_max = numeric_limits<T>::max();
#endif

//  fast alloc
#if 0
int const MAX_MEM = 1e8;
int mpos = 0;
char mem[MAX_MEM];
void* operator new(size_t n) {
  mpos += n;
  return (void*)(mem + mpos - n);
}
void operator delete (void*) noexcept {}
#endif

//  pragmas
#if 0
#pragma GCC optimize("Ofast")
#pragma GCC target("sse,sse2,sse3,ssse3,sse4")
#pragma GCC optimize("unroll-loops")
#endif

int main() {
#ifdef GOLIKOV
  assert(freopen("in", "rt", stdin));
  auto _clock_start = chrono::high_resolution_clock::now();
#endif
  ios::sync_with_stdio(false);
  cin.tie(nullptr);

  int n, k;
  cin >> n >> k;

  vector<bool> bad(10);
  for (int i = 0; i < k; ++i) {
    int d;
    cin >> d;
    bad[d] = true;
  }

  auto check = [&](int n) {
    while (n) {
      if (bad[n % 10]) return false;
      n /= 10;
    }
    return true;
  };

  for (; !check(n); ++n) {}
  cout << n << '\n';

#ifdef GOLIKOV
  cerr << "Executed in " << chrono::duration_cast<chrono::milliseconds>(
      chrono::high_resolution_clock::now()
          - _clock_start).count() << "ms." << endl;
#endif
  return 0;
}