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 PHP7 (7.0.15) (judge verdict: Wrong Answer)

<?php
fscanf(STDIN, "%s", $S);
fscanf(STDIN, "%d", $K);

if ($K === 1) {
    echo cnt($S);
} else {
    $c1 = cnt($S);
    $c2 = cnt($S . $S);
    echo ($c2 - $c1) * ($K - 1) + $c1;
}

function cnt($S) {
    $len = strlen($S);
    $ret = 0;
    $tmp = 0;
    for ($i = 1; $i < $len; $i++) {
        if ($S[$i - 1] === $S[$i]) {
            $tmp++;
        }
        if ($S[$i - 1] !== $S[$i] || $len - 1 === $i) {
            $ret += intdiv($tmp + 1, 2);
            $tmp = 0;
        }
    }
    return $ret;
}