Problem:
Score : 300 points

Problem Statement

Given is a string S. Let T be the concatenation of K copies of S.
We can repeatedly perform the following operation: choose a character in T and replace it with a different character.
Find the minimum number of operations required to satisfy the following condition: any two adjacent characters in T are different.

Constraints

1 \leq |S| \leq 100

S consists of lowercase English letters.

1 \leq K \leq 10^9

K is an integer.

Input

Input is given from Standard Input in the following format:

S
K

Output

Print the minimum number of operations required.

Sample Input 1

issii
2

Sample Output 1

4

T is issiiissii. For example, we can rewrite it into ispiqisyhi, and now any two adjacent characters are different.

Sample Input 2

qq
81

Sample Output 2

81

Sample Input 3

cooooooooonteeeeeeeeeest
999993333

Sample Output 3

8999939997

Solution in PHP (7.4.4) (judge verdict: Wrong Answer)

<?php
list($s) = strs();
$n = strlen($s);
list($k) = ints();
$a = substr_info($s);
$cnt = 0;
foreach ($a as $i => list($v, $c)) {
    if ($i === count($a) - 1 && $s[0] === $s[$n - 1])
        $cnt += intdiv($c + 1, 2) * ($k - 1) + intdiv($c, 2);
    else $cnt += intdiv($c, 2) * $k;
}
echo $cnt;
// 文字列の要素と連続数を格納した配列を返す
function substr_info(string $s): array
{
    $n = strlen($s);
    $cnt = 0;
    for ($i = 0; $i < $n; $i++) {
        $cnt++;
        if ($i === $n - 1 || $s[$i] !== $s[$i + 1]) {
            $_s[] = [$s[$i], $cnt];
            $cnt = 0;
        }
    }
    return $_s;
}
function ints()
{
    return array_map('intval', explode(' ', trim(fgets(STDIN))));
}
function strs()
{
    return explode(' ', trim(fgets(STDIN)));
}