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
  input = sys.stdin.readline
  
  
  t=int(input())
  for tests in range(t):
      n,k=map(int,input().split())
  
      S=str(n)
  
      x=""
      ANS=int(str(min(9,int(S[0])+1))*len(S))
  
      for i in range(len(S)):
          x+=S[i]
  
          if len(set(x))>k:
              break
  
          #print(x)
  
          if i==len(S)-1:
              ANS=n
  
          if i!=len(S)-1:
              j=S[i+1]
  
              for t in sorted(x):
                  if t>j:
                      break
              if t>j:
  
                  y=x+t
  
                  #print(x,t,y)
  
                  if len(set(y))==k:
                      u=min(y)
                  else:
                      u="0"
  
                  ANS=min(ANS,int(y+u*(len(S)-len(y))))
              
          if i!=len(S)-1:
              j=S[i+1]
  
              if j=="9":
                  continue
  
              y=x+str(int(j)+1)
  
              if len(set(y))>k:
                  continue
  
              if len(set(y))==k:
                  u=min(y)
              else:
                  u="0"
  
              ANS=min(ANS,int(y+u*(len(S)-len(y))))
  
          #print(x)
  
  
  
      print(ANS)
              
  
      
  