description: It is a complicated version of problem F1. The difference between them is the constraints (F1: k ≤ 2, F2: k ≤ 10).
  
  You are given an integer n. Find the minimum integer x such that x ≥ n and the number x is k-beautiful.
  
  A number is called k-beautiful if its decimal representation having no leading zeroes contains no more than k different digits. E.g. if k = 2, the numbers 3434443, 55550, 777 and 21 are k-beautiful whereas the numbers 120, 445435 and 998244353 are not.
  
  Input
  
  The first line contains one integer t (1 ≤ t ≤ 10^4) — the number of test cases. Then t test cases follow.
  
  Each test case consists of one line containing two integers n and k (1 ≤ n ≤ 10^9, 1 ≤ k ≤ 10).
  
  Output
  
  For each test case output on a separate line x — the minimum k-beautiful integer such that x ≥ n.
  
  Example
  
  Input
  
  
  6
  2021 3
  177890 2
  34512 3
  724533 4
  998244353 1
  12345678 10
  
  
  Output
  
  
  2021
  181111
  34533
  724542
  999999999
  12345678
solution: import java.io.*;
  import java.util.*;
  
  import static java.lang.Math.min;
  import static java.util.Arrays.fill;
  
  public class Round {
      FastScanner in;
      PrintWriter out;
  
      private void solve() throws IOException {
          char[] s = in.next().toCharArray();
          for (int i = 0; i < s.length; i++)
              s[i] -= '0';
  
          int k = in.nextInt();
  
          int alpha = 10;
          int[] cnt = new int[alpha];
          int[] pos = new int[alpha];
          int ss = 0;
  
          for (char c : s) {
              if (cnt[c] == 0)
                  pos[c] = ss++;
              cnt[c]++;
          }
  
          /*
          for (int i = 0; i < s.length; i++)
              s[i] += '0';
          out.print(new String(s) + " " + k + " ->");
          for (int i = 0; i < ss; i++) {
              if (i == k)
                  out.print(" | ");
              out.print(st[i]);
          }
          out.println();
          for (int i = 0; i < s.length; i++)
              s[i] -= '0';
          */
  
          fill(cnt, 0);
          ss = 0;
          for (int i = 0; i < s.length; i++) {
              if (cnt[s[i]]++ == 0)
                  ss++;
              if (ss <= k)
                  continue;
  
              while (ss > k) {
                  if (--cnt[s[i]] == 0)
                      ss--;
  
                  s[i]++;
                  while (s[i] == alpha) {
                      i--;
                      if (--cnt[s[i]] == 0)
                          ss--;
                      s[i]++;
                  }
  
                  if (cnt[s[i]]++ == 0)
                      ss++;
              }
  
              int min = s[0];
              for (int j = 0; j <= i; j++)
                  min = min(min, s[j]);
              for (int j = i + 1; j < s.length; j++)
                  s[j] = ss < k ? 0 : (char) min;
              break;
          }
  
          for (int i = 0; i < s.length; i++)
              s[i] += '0';
          out.println(new String(s));
      }
  
      class FastScanner {
          StringTokenizer st;
          BufferedReader br;
  
          FastScanner(InputStream s) {
              br = new BufferedReader(new InputStreamReader(s));
          }
  
          String next() throws IOException {
              while (st == null || !st.hasMoreTokens())
                  st = new StringTokenizer(br.readLine());
              return st.nextToken();
          }
  
          int nextInt() throws IOException {
              return Integer.parseInt(next());
          }
  
          long nextLong() throws IOException {
              return Long.parseLong(next());
          }
  
          double nextDouble() throws IOException {
              return Double.parseDouble(next());
          }
      }
  
      private void run() throws IOException {
          in = new FastScanner(System.in);
          out = new PrintWriter(System.out);
  
          for (int t = in.nextInt(); t-- > 0; )
              solve();
  
          out.flush();
          out.close();
      }
  
      public static void main(String[] args) throws IOException {
          new Round().run();
      }
  }
  