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 x d digits long or (2 x 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 n² = 25. We split that into two strings and convert them back to integers 2 and 5. We test , so this is not a modified Kaprekar number. If n = 9, still d = 1, and n² = 81. This gives us 1 + 8 = 9, the original n.

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 p and q where p is lower than q, write a program to print the modified Kaprekar numbers in the range between p and q, 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 p. The second line contains the upper integer limit q.

Note: Your range should be inclusive of the limits.

Constraints

0 < p < q < 100000

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
2

1
100

Sample Output

1

1 9 45 55 99

Explanation

1, 9, 45, 55, and 99 are the Kaprekar Numbers in the given range.

Solution

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// Complete the kaprekarNumbers function below.
function kaprekarNumbers(p, q) {
  let result = Array.from(
    { length: q - p + 1 },
    (value, index) => index + p
  ).reduce((target, value, index) => {
    let square = `${value ** 2}`;
    let right = +square.substring(
      square.length - `${value}`.length,
      square.length
    );
    let left = +square.substring(0, square.length - `${value}`.length);

    left + right == value && target.push(value);

    return target;
  }, []);

  console.log(!result.length ? "INVALID RANGE" : result.join(" "));
}