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- Modified Kaprekar Numbers

# Modified Kaprekar Numbers

# 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 with digits. We square to arrive at a number that is either digits long or digits long. Split the string representation of the square into two parts, and . The right hand part, must be digits long. The left is the remaining substring. Convert those two substrings back to integers, add them and see if you get .

For example, if , then . We split that into two strings and convert them back to integers and . We test , so this is not a modified Kaprekar number. If , still , and . This gives us , the original .

**Note:** r may have leading zeros.

Here's an explanation from Wikipedia about the **ORIGINAL** Kaprekar Number (spot the difference!):

In mathematics, a Kaprekar number for a given base is a non-negative integer, the representation of whose square in that base can be split into two parts that add up to the original number again. For instance, 45 is a Kaprekar number, because 45² = 2025 and 20+25 = 45.

Given two positive integers and where is lower than , write a program to print the modified Kaprekar numbers in the range between and , inclusive.

**Function Description**

Complete the *kaprekarNumbers* function in the editor below. It should print the list of modified Kaprekar numbers in ascending order.

kaprekarNumbers has the following parameter(s):

*p*: an integer*q*: an integer

**Input Format**

The first line contains the lower integer limit .

The second line contains the upper integer limit .

**Note**: Your range should be inclusive of the limits.

**Constraints**

**Output Format**

Output each modified Kaprekar number in the given range, space-separated on a single line. If no modified Kaprekar numbers exist in the given range, print `INVALID RANGE`

.

**Sample Input**

```
1
100
```

**Sample Output**

1 9 45 55 99

**Explanation**

, , , , and are the Kaprekar Numbers in the given range.