from math import comb

def pascal(n, left, right):
  i = 1
  result = [[left, right]]

  while i < n:
    prev_row = result[-1]
    result.append(
      [left ** (i+1)]
    + [comb(i+1, j+1) * (left ** (len(prev_row)-j-1)) * (right ** (j+1)) for j in range(len(prev_row)-1)]
    + [right ** (i+1)])

    i += 1

  return result

def pretty_print_pascal(triangle):
  for i, row in enumerate(triangle):
    print(f'{i+1}.\t{row}')

def pretty_print_row(row):
  for i, coefficient in enumerate(row):
    print(f'{coefficient}\tx^{len(row)-i-1}\ty^{i}')


if __name__ == "__main__":

  print('a. ')
  pretty_print_row(pascal(12, 1, 1)[-1])
  print()

  print('b. ')
  pretty_print_row(pascal(12, 1, 2)[-1])
  print()

  print('c. ')
  pretty_print_row(pascal(12, 2, -3)[-1])