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: # by the authority of GOD     author: manhar singh sachdev #
  
  import os,sys
  from io import BytesIO, IOBase
  from collections import Counter
  
  def comp(arr1,arr2):
      # arr1 = ans
      if len(arr1) > len(arr2):
          return 1
      if len(arr1) < len(arr2):
          return 0
      for i,j in zip(arr1,arr2):
          if i > j:
              return 1
          if i < j:
              return 0
  
  def main():
      for _ in range(int(input())):
          n,k = input().split()
          k = int(k)
          n = list(map(int,n))
          if len(Counter(n)) <= k:
              print(''.join(map(str,n)))
              continue
          le = len(n)
          ans = [1]+[0]*le if k >= 2 else [1]*(le+1)
          curr = []
          mini = float("inf")
          uni = Counter()
          for idx,i in enumerate(n):
              if len(uni) > k:
                  break
              for j in range(i+1,10):
                  uni[j] += 1
                  if len(uni) < k:
                      poss = curr + [j] + [0]*(le-idx-1)
                      if comp(ans,poss):
                          ans = poss
                  elif len(uni) == k:
                      mini1 = min(mini,j)
                      poss = curr + [j] + [mini1]*(le-idx-1)
                      if comp(ans,poss):
                          ans = poss
                  uni[j] -= 1
                  if not uni[j]:
                      del uni[j]
              mini = min(mini,i)
              curr += [i]
              uni[i] += 1
          print(''.join(map(str,ans)))
  
  # Fast IO Region
  BUFSIZE = 8192
  class FastIO(IOBase):
      newlines = 0
      def __init__(self, file):
          self._fd = file.fileno()
          self.buffer = BytesIO()
          self.writable = "x" in file.mode or "r" not in file.mode
          self.write = self.buffer.write if self.writable else None
      def read(self):
          while True:
              b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
              if not b:
                  break
              ptr = self.buffer.tell()
              self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
          self.newlines = 0
          return self.buffer.read()
      def readline(self):
          while self.newlines == 0:
              b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
              self.newlines = b.count(b"\n") + (not b)
              ptr = self.buffer.tell()
              self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
          self.newlines -= 1
          return self.buffer.readline()
      def flush(self):
          if self.writable:
              os.write(self._fd, self.buffer.getvalue())
              self.buffer.truncate(0), self.buffer.seek(0)
  class IOWrapper(IOBase):
      def __init__(self, file):
          self.buffer = FastIO(file)
          self.flush = self.buffer.flush
          self.writable = self.buffer.writable
          self.write = lambda s: self.buffer.write(s.encode("ascii"))
          self.read = lambda: self.buffer.read().decode("ascii")
          self.readline = lambda: self.buffer.readline().decode("ascii")
  sys.stdin, sys.stdout = IOWrapper(sys.stdin), IOWrapper(sys.stdout)
  input = lambda: sys.stdin.readline().rstrip("\r\n")
  if __name__ == "__main__":
      main()