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 = input().split()
      k = int(k)
  
      cnt = Counter(n)
      if len(cnt) <= k:
          print(n)
          return
      
      cnt = Counter()
  
      ans = []
      for c in n:
          if c in cnt:
              cnt[c] += 1
              ans.append(c)
              continue
          if len(cnt) == k: break
          cnt[c] += 1
          ans.append(c)
      
      i = len(ans)
      for j in range(int(n[i])+1, 10):
          if str(j) in cnt:
              ans.append(str(j))
              m = min(cnt.keys())
              while len(ans) < len(n):
                  ans.append(m)
              print("".join(ans))
              return
      
      while i >= 0:
          i -= 1
          c = ans[i]
          cnt[c] -= 1
          if cnt[c] == 0:
              del cnt[c]
          
          for nxt in range(int(c)+1, 10):
              nxt = str(nxt)
              if nxt not in cnt:
                  if len(cnt) == k: continue
              cnt[nxt] += 1
              ans[i] = nxt
              if len(cnt) < k:
                  cnt["0"] += 1
              m = min(cnt.keys())
              for j in range(i+1, len(ans)):
                  ans[j] = m
              while len(ans) < len(n):
                  ans.append(m)
              print("".join(ans))
              return
      assert 1 < 0
  
  
  
  for _ in range(int(input()) ):
      solve()
  
  