code: def egypt_takenouchi(x, y):
      # assumes gcd(x, y) == 1
      # special cases for 3/y
      if x == 3:
          if y % 2 == 0:
              return [y // 2, y]
          i = (y - 1) // 2
          j = i + 1
          k = j + i
          return [j, k, j * k]
      l = [y] * x
      while len(l) != len(set(l)):
          l.sort()
          for i in range(len(l) - 1):
              if l[i] == l[i + 1]:
                  break
          k = l[i]
          if k % 2 == 0:
              l[i] = l[i] // 2
              del l[i + 1]
          else:
              l[i], l[i + 1] = (k + 1) // 2, k * (k + 1) // 2
      return sorted(l)
  
file_path: sympy/sympy/ntheory/egyptian_fraction.py
imports: from sympy.core.containers import Tuple
  from sympy.core.numbers import Integer, Rational
  from sympy.core.singleton import S
  import sympy.polys
  from math import gcd
label_desc: Use image node_id 4 for calling a global function with example usage: egypt_takenouchi(x, y) and returns: sorted, list, list