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 java.text.*;
  import java.math.*;
  
  public class Main {
  	public static void main(String[] args) throws IOException{
  		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
          StringBuilder sb = new StringBuilder();
  		int t = Integer.parseInt(br.readLine());
          while(t-- > 0){
              StringTokenizer st = new StringTokenizer(br.readLine());
              int n = Integer.parseInt(st.nextToken());
              int k = Integer.parseInt(st.nextToken());
              StringBuilder res = new StringBuilder();
              HashMap<Integer, Integer> map = new HashMap<Integer, Integer>();
              findResult(n + "", k, res, 0, map);
              sb.append(res);
              sb.append("\n");
          }
  		System.out.print(sb);
  	}
  	public static boolean findResult(String s, int k, StringBuilder result, int index, HashMap<Integer, Integer> map){
  	    if(result.length() > 0 && Integer.parseInt(s.substring(0, index)) > Integer.parseInt(result.toString()))
  	        return false;
  	    if(map.size() <= k && result.length() > 0){
  	        if(s.charAt(s.length() - 1) == ' ')
  	            s = s.substring(0, s.length() - 1);
  	       // System.out.println(s);
  	        if(Integer.parseInt(result.toString()) >= Integer.parseInt(s))
  	            return true;
  	    }
  	    for(int i = 0; i < 10; i++){
  	        if(index == 0 && i == 0)
  	            continue;
  	        if(map.size() == k && !map.containsKey(i))
  	            continue;
  	        map.put(i, map.getOrDefault(i, 0) + 1);
  	        result.append(i);
  	       // if(s.equals("177890")){
  	       //    // System.out.println("size " + set.size() + " " + map);
  	       //     System.out.println(result);
  	       // }
  	        if(findResult(s, k, result, index + 1, map))
  	            return true;
  	        result.deleteCharAt(result.length() - 1);
  	        map.put(i, map.get(i) - 1);
  	        if(map.get(i) == 0)
  	            map.remove(i);
  	    }
  	    return false;
  	}
  }
  
  
  