Egyptian Fractions

'''
Good morning! Here's your coding interview problem for today.
This problem was asked by Palantir.
The ancient Egyptians used to express fractions as a sum of several terms where each numerator is one.
For example, 4 / 13 can be represented as 1 / 4 + 1 / 18 + 1 / 468.
Create an algorithm to turn an ordinary fraction a / b, where a < b, into an Egyptian fraction.
'''
import random

# FUNCTION 1
def egyptian(a, b):
    if a != int(a) or b != int(b) or a <= 0 or b <= 0 or a >= b:
        print("Error while using function " + egyptian.__name__)
    # Now, I will begin the scanning
    SUM = 0
    target = a / b
    counter = 2
    LIMIT = 10 ** 5
    numbers = list()
    while SUM < target and counter <= LIMIT:
        if target - SUM >= 1 / counter:
            SUM += 1 / counter
            numbers.append(counter)
        counter += 1
    return numbers


# FUNCTION 2
def prettyPrint(a, b):
    numbers = egyptian(a, b)
    result = ""
    for i in range(len(numbers)):
        if i != len(numbers) - 1:
            result += "1/" + str(numbers[i]) + " + "
        else:
            result += "1/" + str(numbers[i])
    print(str(a) + "/" + str(b) + " = " + result)

# MAIN FUNCTION
prettyPrint(7, 12)
prettyPrint(1, 12)
prettyPrint(5, 6)
prettyPrint(2, 3)
prettyPrint(4, 13)
prettyPrint(3, 10)
prettyPrint(random.randrange(2, 10), random.randrange(11, 20))