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: Accepted)

chomp($s = <>);
chomp($n = <>);

$t = "";
@str = ();
for (split(//, $s)){
	if($t ne ""){
		if($_ eq substr($t,0,1)){
			$t .= $_;
		}else{
			push(@str, $t);
			$t = $_;
		}
	}else{
		$t = $_;
	}
}
push(@str, $t);

$cnt = 0;
if(scalar(@str) == 1){
	$cnt = int(length($s) * $n / 2);
}else{
	for $i (1 .. $#str - 1){
		$cnt += int(length($str[$i]) / 2);
	}
	$cnt = $cnt * $n;

	if(substr($str[0],0,1) eq substr($str[$#str],0,1)){
		$cnt += int((length($str[0]) + length($str[$#str])) / 2) * ($n - 1);
		$cnt += int(length($str[0]) / 2);
		$cnt += int(length($str[$#str]) / 2);
	}else{
		$cnt += int(length($str[0]) / 2) * $n;
		$cnt += int(length($str[$#str]) / 2) * $n;
	}

}

print "$cnt\n";