Multiply Big Number

<?php

$num1 = readline();
$num2 = intval(readline());

if ($num1 === '0' || $num2 === 0) {
    echo '0';
    return;
}

$digits = [];

for ($i = 0; $i < strlen($num1); $i++) {
    $digits[] = intval($num1[$i]);
}

$remainder = 0;
$result = $digits;

for ($j = 0; $j < $num2 - 1; $j++) {
    for ($k = count($digits) - 1; $k >= 0; $k--) {
        $sum = $result[$k] + $digits[$k] + $remainder;

        if ($sum > 9 && $k !== 0) {
            $result[$k] = $sum % 10;
            $remainder = 1;
        } else {
            $result[$k] = $sum;
            $remainder = 0;
        }
    }
}

echo implode('', $result);