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 Perl (v5.18.2) (judge verdict: Wrong Answer)

chomp($s=<>);
chomp($k=<>);
@ary=split//,$s;
$num=1;
for($i=0;$i<$#ary;$i++){
	if($ary[$i] eq $ary[$i+1]){
    	$num++;
    }else{
    	$cnt+=int($num/2);
        $num=1;
    }
}
if($num>=2){
	$cnt+=int($num/2);
	if($ary[0] eq $ary[$#ary] && $num%2==1){
    	$ans=$cnt*$k+$k-1;
    }else{
    	$ans=$cnt*$k;
    }
}elsif($ary[0] eq $ary[$#ary]){
	$cnt++;
    if($k==1){
    	$cnt--;
    }
    $ans=$cnt*$k;
}else{
	$ans=$cnt*$k;
}
print $ans;