code: def _dup_decompose(f, K):
      """Helper function for :func:`dup_decompose`."""
      df = len(f) - 1
  
      for s in range(2, df):
          if df % s != 0:
              continue
  
          h = _dup_right_decompose(f, s, K)
  
          if h is not None:
              g = _dup_left_decompose(f, h, K)
  
              if g is not None:
                  return g, h
  
      return None
  
imports: from sympy.polys.densearith import dup_add_term, dmp_add_term, dup_lshift, dup_add, dmp_add, dup_sub, dmp_sub, dup_mul, dmp_mul, dup_sqr, dup_div, dup_rem, dmp_rem, dmp_expand, dup_mul_ground, dmp_mul_ground, dup_quo_ground, dmp_quo_ground, dup_exquo_ground, dmp_exquo_ground
  from sympy.polys.densebasic import dup_strip, dmp_strip, dup_convert, dmp_convert, dup_degree, dmp_degree, dmp_to_dict, dmp_from_dict, dup_LC, dmp_LC, dmp_ground_LC, dup_TC, dmp_TC, dmp_zero, dmp_ground, dmp_zero_p, dup_to_raw_dict, dup_from_raw_dict, dmp_zeros
  from sympy.polys.polyerrors import MultivariatePolynomialError, DomainError
  from sympy.utilities import variations
  from math import ceil, log
label_desc: Use image node_id 37 for calling a global function with example usage: _dup_decompose(f, K) and returns: None, g,  h