from itertools import combinations

def generate_cage_combinations(total, area, excluded_numbers):
    # Generate cage combinations for a given total and area, excluding the specified numbers
    numbers = list(range(1, 10))
    cage_combinations = []

    # Generate all possible combinations of numbers from 1 to 9 with the given area
    for combination in combinations(numbers, area):
        if sum(combination) == total:
            combination_digits = [int(digit) for number in combination for digit in str(number)]
            if all(digit not in excluded_numbers for digit in combination_digits):
                formatted_combination = ' '.join(str(num) for num in combination)
                cage_combinations.append(formatted_combination)

    return cage_combinations


while True:
    print('List of Modes')
    print('For cage overlapping box press A')
    print('For cage combinations press B')
    print('For calculator press C')
    print('To return to the main menu, type zero (0) as your input')
    opt = input('Mode? ')

    if 'a' in opt.lower():
        print('For cages that overlap more than one box')
        print("\n")
        print("____________________ ")
        print("_________ ____ |     ")
        print("| N      ||B  ||     ")
        print("|        ||   ||     ")
        print("|        ||___||     ")
        print("|        |_____|____ ")
        print("|              | A  |")
        print("|______________|____|")
        print("               |     ")
        print("\n")

        while True:
            grid_base_number = int(input('Total cage value (N)? '))
            if grid_base_number == 0:
                print("\n")
                break
            else:
                if grid_base_number >= 45:
                    result_a = grid_base_number - 45
                    result_b = 0
                else:
                    result_a = 0
                    result_b = 45 - grid_base_number

                print('N = ' + str(grid_base_number))

                # Format and count up for result_a
                a_values = ' '.join('{:>2}'.format(result_a + i) for i in range(19))
                print('A = ' + a_values)

                # Format and count up for result_b
                b_values = ' '.join('{:>2}'.format(result_b + i) for i in range(19))
                print('B = ' + b_values)

                print("\n")
                continue


    elif 'b' in opt.lower():
        print('For Cage Combinations')
        print("\n")
        print(" ___________________ ")
        print("|      |      |     |")
        print("|¦¯¯¯¯¯|¯¯¯¯¯¦|     |")
        print("|¦ N   |     ¦|     |")
        print("| -----|----- |     |")
        print("|                    ")
        print("      (N)sum /range  ")
        print("\n")

        while True:
            total = int(input('Cage Total? '))
            if total == 0:
                print("\n")
                break
            else:
                area = int(input('Cage Area? '))

                if area == 0:
                    print("\n")
                    break
                else:
                    excluded_numbers_input = input('Numbers to exclude (leave blank if none): ')
                    excluded_numbers = [int(digit) for digit in excluded_numbers_input if digit.isdigit()]
                    cage_combinations = generate_cage_combinations(total, area, excluded_numbers)
                    print("  " + '   '.join(cage_combinations))
                    print("\n")

                    further_details = input('Would you like further details? (y/n) ')
                    if further_details.lower() == 'y':
                        n_value = total
                        b_value = int(input('Enter the value for B: '))
                        a_value = n_value - b_value if (n_value + b_value) <= 45 else 45 - (n_value + b_value)
                        a_values = ' '.join('{:>2}'.format(a_value + i) for i in range(19))
                        print('A = ' + a_values)

                    print("\n")
                    continue
                
    elif 'c' in opt.lower():
        print('Calculator')
        print("\n")

        while True:
            expression = input('Enter an expression (+ or -): ')
            if expression == '0':
                print('Returning to the main menu...')
                print("\n")
                break

            try:
                result = eval(expression)
                print('Result: ' + str(result))
                print("\n")
            except:
                print('Invalid expression')
                continue

    elif opt == '0':
        print('Returning to the main menu...')
        print("\n")
        continue

    else:
        print('Invalid mode')
        continue