#########################
# SHP Computer Programming in Python 
# February 2nd 2019
# Name : Kelly Ryu
#
# File contains algorithm for calculating the product of two arbitrary integers
#########################


again = "Yes"
while again == "Yes":

    # Ask user to input two integers to be multiplied

    first = int(input('Write the first integer to be multiplied: '))
    second = int(input('Write the second integer to be multiplied: '))

    # If second number is odd, add "first" to the list of numbers to be added

    if second % 2 == 1:
        product = first 
    else:
        product = 0

    # Until second number reaches 0 or 1, multiply "first" by 2 
    # and divide "second" by 2
    # Add multiple of first number to list if result of division is 1

    while second > 1:
        second = second // 2
        first = 2 * first
        if second % 2 == 1:
            product = product + first

    # Print result of all necessary addition as the final product

    print("The product is {}.".format(product))
    again = input("Would you like to find another product? (Yes/No): " )