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
  import time
  input = sys.stdin.readline
  def main():
      t = int(input())
      for _ in range(t):
          n, k = list(map(int, input().split()))
          digits = len(str(n))
          first = str(n)[0]
          if digits == 1:
              print(n)
              continue
          if k==1:
              if int(first*digits) >= n:
                  print(first*digits)
              else:
                  print(str(int(first)+1)*digits)
              continue
          m = str(n)
          picked = [first]
          picked_list = [i==int(first) for i in range(10)]
          left = k-1
          res = ''
          big = 0
          maxx = int(first)
          for i in range(digits):
              if big:
                  if left == 1:
                      res += (digits-i)*'0'
                  else:
                      res += (digits - i) * str(min([int(j) for j in picked]))
                  break
  
              if left == 0:
                  minpicked = str(min([int(j) for j in picked if int(j) >= int(m[i])]))
                  if int(minpicked) > int(m[i]):
                      res += minpicked
                      big = 1
                      continue
                  if int(res + m[i] + str(maxx)*(digits-i-1)) >= n:
                      res += minpicked
                      continue
                  else:
                      res += str(sorted([int(j) for j in picked if int(j) >= int(m[i])])[1])
                      big = 1
                      continue
  
              if picked_list[int(m[i])]:
                  res += m[i]
                  continue
              if left >= 2:
                  maxx = max(int(m[i]), maxx)
                  picked.append(m[i])
                  picked_list[int(m[i])] = True
                  left -= 1
                  res += m[i]
                  continue
              if left == 1:
                  if int(res + m[i] + str(max(maxx, int(m[i])))*(digits-i-1)) >= n:
                      maxx = max(int(m[i]), maxx)
                      picked.append(m[i])
                      picked_list[int(m[i])] = True
                      left = 0
                      res += m[i]
                      continue
                  else:
                      big = 1
                      if picked_list[int(m[i]) + 1]:
                          res += str(int(m[i]) + 1)
                      else:
                          left -= 1
                          picked.append(str(int(m[i])+1))
                          picked_list[int(m[i])+1] = True
                          maxx = max(int(m[i])+1, maxx)
                          res += str(int(m[i])+1)
                      continue
          print(res)
  main()
  
  
  
  