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: def find_nearest(s, k):
      ln = len(s)
      if max(s[:ln-1]) > s[ln-1]:
          x = list(set(s[:ln-1]))
          x.sort()
          for it in x:
              if it > s[-1]:
                  # s[-1] = it
                  s = s[:ln-1] + it
                  return s
      else:
          # 1778
          for i in range(ln-1, -1, -1):
              x = s[:i]
              while (x[-1] <'9'):
                  x = str(int(x)+1)
                  if len(set(x)) <=k:
                      if len(set(x)) == k:
                          x = x + (ln-len(x)) * min(set(x))
                          return x
                      else:
                          x = x + (ln-len(x)) * '0'
                          return x
  
          
  def solve(s, k):
      if len(set(str(s))) <=k:
          return s
      s = str(s)
      for i in range(len(s)):
          if len(set(s[:i+1])) > k:
              break
      i+=1
      x = s[:i]
      # print(x)
      x = find_nearest(x, k)
      # print(x)
      # while len(set(x)) >k:
      #     x = str(int(x) +1)
      ans = x + (len(s)-i) * min(set(x))
      return ans
      # k = s[:i]
          
  
  n = int(input())
  for _ in range(n):
      s, k = [int(i) for i in input().split()]
      print(solve(s,k))
  
  """
  1
  131455 2 -> 1331
  177890 2 -> 1
  1314 2 -> 1331
  """