input: def is_valid_numeric_string(string: str) -> bool:
      """ Checks if the given string is a valid numeric string using a regular expression.
      >>> is_valid_numeric_string('123456789')
      True
      >>> is_valid_numeric_string('123abc456')
      False
      """
      import re
      pattern = '^[0-9]+$'
      result = re.match(pattern, string)
      return bool(result)
output:     import re
      pattern = '^[0-9]+$'
      result = re.match(pattern, string)
      return bool(result)