Modified Kaprekar Numbers

A modified Kaprekar number is a positive whole number with a special property. If you square it, then split the number into two integers and sum those integers, you have the same value you started with.

Consider a positive whole number n with d digits. We square n to arrive at a number that is either 2 * d digits long or (2 * d) - 1 digits long. Split the string representation of the square into two parts, l and r. The right-hand part, r must be d digits long. The left is the remaining substring. Convert those two substrings back to integers, add them and see if you get n.

For example, if n=5, d=1, then n squared = 25 . We split that into two strings and convert them back to integers 2 and 5. We test 2+5=7=5, so this is not a modified Kaprekar number. If n=9, d=1, and n squared = 81. This gives us 1+8=9, the original n.

Note that r may have leading zeros.

Complete the kaprekarNumbers() method. It should return the list of modified Kaprekar numbers in ascending order. kaprekarNumbers() has the following parameter(s):

• p: an integer representing the lower integer limit.
• q: an integer representing the upper integer limit.

Examples

kaprekarNumbers(1, 10) ➞ "1 9"

kaprekarNumbers(100, 300) ➞ "297"

kaprekarNumbers(1, 100) ➞ "1 9 45 55 99"

Notes

• Upper and lower ranges should be inclusive of the limits.
• If no modified Kaprekar numbers exist in the given range, return "INVALID RANGE".