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 sys
  from sys import stdin
  
  def solve(n,k):
  
      s = set()
      ans = []
  
      for i in range(len(n)):
  
          dig = n[i]
          if (len(s) == k) and (dig not in s):
  
              bigmin = None
              for c in s:
                  if dig < c:
                      if bigmin == None:
                          bigmin = c
                      else:
                          bigmin = min(bigmin,c)
              
              if bigmin == None: #padding zero
                  divser = 10**(len(n)-i)
                  nex = (int(n) // divser + 1) * divser
                  return solve(str(nex),k)
              
              else:
                  ans.append(bigmin)
                  allmin = min(s)
                  while len(ans) < len(n):
                      ans.append(allmin)
                  return "".join(ans)
  
          s.add(dig)
          ans.append(dig)
  
      return "".join(ans)
  
      
  
  tt = int(stdin.readline())
  
  ANS = []
  for loop in range(tt):
  
      n,k = (stdin.readline()[:-1]).split()
      k = int(k)
  
      ANS.append(solve(n,k))
  
  print ("\n".join(ANS))