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
  n = ''
  k = l = 0
  d = [0] * 9
  
  def dfs(cur, dset):
      p = len(cur)
      if p == l: return cur
      if cur > n: nd = 0
      else: nd = int(n[p])
      for i in range(nd, 10):
          if i in dset:
              r = dfs(cur+str(i), dset)
              if r != -1: return r
          else:
              if len(dset) < k:
                  r = dfs(cur+str(i), dset|set([i]))
                  if r != -1: return r
      return -1
  
  
  for _ in range(int(sys.stdin.readline())):
      n, k = sys.stdin.readline().split()
      k = int(k)
      l = len(n)
      sys.stdout.write(dfs('', set())+'\n')
  