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 number(L):
      r = 0
      for d in L:
          r = r * 10 + int(d)
      return r
  
  def go(n, i, D, eq):
      if i == len(n):
          return True, []
  
      if eq:
          for d in D:
              if n[i] == d:
                  flag, x = go(n, i + 1, D, True)
                  if flag:
                      return True, [d] + x
              if n[i] < d:
                  flag, x = go(n, i + 1, D, False)
                  if flag:
                      return True, [d] + x
  
          return False, []
      else:
          flag, x = go(n, i + 1, D, False)
          return True, [D[0]] + x
  
  
  def find(n, k):
      if len(set(n)) == 1:
          return n
      
      D = []
      for d in map(int, n):
          if d not in D:
              D.append(d)
  
      if len(D) <= k:
          return n
  
      U = [D[: k]]
  
      E = D[: k]
      if (E[-1] + 1) in E:
          E[-1] = 0
      else:
          E[-1] = (E[-1] + 1) % 10
      U.append(E)
  
  
      r = 10**20
      for digits in U:
          x = []
          digits.sort()
          flag, x = go(list(map(int, n)), 0, digits, True)
          if flag:
              r = min(r, number(x))
  
      return r
  
  T = int(input())
  for _ in range(T):
      n, k = input().split(' ')
      k = int(k)
  
                  
      print(find(n, k))
  