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: for i in range(int(input())):
      a,k=input().split()
      k=int(k)
      k0=k
      b=[0]*10
      a=[int(i) for i in a]
      j=0
      m=9
      mx=0
      for i in a:
          if b[i]==0:
              k-=1
          if k<0:
              break
          j+=1
          b[i]+=1
          m=min(m,i)
          mx=max(mx,i)
      if j==len(a): 
          print(*a,sep='')
          continue
      for i in range(a[j]+1,10):
          if b[i]:
              a[j]=i
              for k in range(j+1,len(a)):
                  a[k]=m
              break
      else:
          b1=[0]*10
          j1=j
          for i in range(j1):
              if b1[a[i]]==0 or a[i]!=mx:
                  j=i+1
                  b1[a[i]]=1
          if b[a[j-1]]==1 or a[j-1]==mx:
              a[j-1]+=1
          else:
              while b[a[j-1]+1]==0:
                  a[j-1]+=1
              a[j-1]+=1
          b=[0]*10
          for i in range(j):
              b[a[i]]+=1
          if 10-b.count(0)<k0:
              for i in range(j,len(a)):
                  a[i]=0
          else:
              m=9
              for i in range(10):
                  if b[i]: m=min(m,i)
              for i in range(j,len(a)):
                  a[i]=m
      print(*a,sep='')