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: from collections import Counter
   
  def solve(n, k, cur, cur_set):
      # if len(Counter(str(n))) <= k:
      #     return n
      if len(cur) > len(str(n)) or len(cur_set) > k or cur < str(n)[: len(cur)]:
          return None
      if len(cur) == len(str(n)) and cur >= str(n):
          return cur
      
      for i in range(10):
          if i not in cur_set:
              cur_set.add(i)
              ans = solve(n, k, cur + str(i), cur_set)
              cur_set ^= {i}
          else:
              ans = solve(n, k, cur + str(i), cur_set)
          if ans != None:
              return ans
   
  t = int(input())
  for _ in range(t):
      n, k = map(int, input().split())
      print(solve(n, k, '', set()))