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<?php

function solution(int $x, int $y, int $k, array $a, array $b): int
{
    $widths = length_calc($x, $a);
    $heights = length_calc($y, $b);

    return size($widths, $heights, $k);
}

function length_calc(int $length, array $sections): array
{
    $data = [];

    $count_sections = \count($sections);

    foreach ($sections as $section_id => $section) {
        $data[] = $section - ($sections[$section_id - 1] ?? 0);

        if ($count_sections === $section_id + 1) {
            $data[] = $length - ($sections[$section_id - 1] ?? 0);
        }
    }

    sort($data, SORT_NUMERIC);

    return $data;
}

function size(array $w, array $h, int $o): int
{
    $N = \count($w);

    $start = 1;
    $end = $w[$N - 1] * $h[$N - 1];

    while ($start <= $end) {
        $middle = ($start + $end) >> 1;

        $cal = cal($middle, $w, $h);

        if ($cal >= $o) {
            $start = $middle + 1;
        } else {
            $end = $middle - 1;
        }
    }

    return $start;
}

function cal(int $size, array $w, array $h): int
{
    $N = \count($w);

    if ($w[$N - 1] * $h[$N - 1] <= $size) {
        return 0;
    }

    $result = 0;
    $hIndex = $N - 1;

    foreach (range(0, $N) as $wIndex) {
        while ($hIndex >= 0 && $w[$wIndex] * $h[$hIndex] > $size) {
            $hIndex -= 1;
        }

        $result += $N - 1 - $hIndex;
    }

    return $result;
}

$x = 35;
$y = 38;
$k = 15;

$a = [1, 3, 6, 11, 24, 26, 32];
$b = [1, 5, 8, 13, 16, 22, 26];

echo solution($x, $y, $k, $a, $b);