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.

php

<?php

// Complete the kaprekarNumbers function below.

function kaprekarNumbers($p, $q) {

$cnt = 0;

for($i = $p; $i <= $q; $i++) {

$n2 = $i*$i;

$strn2 = (string)$n2;

$len = strlen($strn2);

if($len%2 == 0) {

$l = substr($strn2,0,$len/2);

$r = substr($strn2,$len/2, $len/2);

} else {

$l = substr($strn2,0,$len/2);

$r = substr($strn2,$len/2, $len/2+1);

}

if(empty($l)) {

$r_i = (int)$r;

if($i == $r_i) {

echo $i. " ";

$cnt++;

}

} else {

$l_i = (int)$l;

$r_i = (int)$r;

if($i == $l_i + $r_i) {

echo $i." ";

$cnt++;

}

}

}

if($cnt == 0) {

echo 'INVALID RANGE';

}

}

$stdin = fopen("php://stdin", "r");

fscanf($stdin, "%d\n", $p);

fscanf($stdin, "%d\n", $q);

kaprekarNumbers($p, $q);

fclose($stdin);