input: 
  from re import match
  
  def is_numeric_string(string: str) -> bool:
      """Checks if the given string is a valid numeric string using a regular expression.
      >>> is_numeric_string('123456789')
      True
      >>> is_numeric_string('abc123')
      False
      """
      pattern = '^[0-9]+$'
      return bool(match(pattern, string))
  
output:     pattern = '^[0-9]+$'
      return bool(match(pattern, string))