input: 
  import re
  
  def is_numeric_string(s: str) -> bool:
      """ Check if the given string is a valid numeric string.
      >>> is_numeric_string('123456789')
      True
      >>> is_numeric_string('abc123')
      False
      >>> is_numeric_string('123.456')
      False
      """
      pattern = '^[0-9]+$'
      result = re.match(pattern, s)
      return bool(result)
  
output:     return result is not None