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
  t = int(input())
  for i in range(t):
      n,k = sys.stdin.readline().split()
      n = n.lstrip("000000000")
      k = int(k)
      L = []
      for s in n:
          if int(s) not in L: L.append(int(s))
      if len(L)<=k: print(n)
      else:
          L = L[:k]
          Num = list(map(int,n))
          ind = Num.index(L[-1])
          maxL = max(L)
          bada = False
          i=0
          while i<len(n):
              if bada: Num[i] = 0
              else:
                  if Num[i]>maxL:
                      bada = True
                      while Num[i]+1>maxL and i>ind: i-=1
                      Num[i]+=1
                      if(i == ind):
                          L[-1]+=1
                          if L[-1] in L[:-1]: L[-1] = 0
                  elif Num[i] not in L:
                      bada = True
              i+=1
              
          L.sort()
          Go = dict()
          ind = 0
          for i in range(L[-1]+1):
              while i>L[ind]:ind+=1
              Go[i] = str(L[ind])
          
          minL = str(L[0])
          bada = False        
          for i in range(len(Num)):
              if bada == True: Num[i] = minL
              else:
                  if (Num[i] not in L): 
                      bada = True
                  Num[i] = Go[Num[i]]
          print(int(''.join(Num)))
                      
                  
          
          