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)

my @A;
my %h;
foreach my $w (split(//o, <STDIN>)){
    chomp($w);
    next if ($w eq '');
    push(@A, $w);
    $h{$w} = 1;
}
my $N = <STDIN>;
chomp($N);

my $numA = $#A;
my $numK = (keys %h);
if ($numK == 1) {
  my $numA2 = $numA+1;
  if ( ($numA2*$N) % 2 ){
    # odd
    my $tmp = $numA2*$N - 1;
    print $tmp/2;
  } else {
    # even
    my $tmp = $numA2*$N;
    print $tmp/2;
  }
  exit 0;
}
my $oddflag = 0;
my $s = $A[0];
my $e = $A[$numA];
if ( $s eq $e ) {
    my $numS = 0;
    foreach my $w (@A){
        if ( $s eq $w ) {
          $numS++;
        } else {
          last;
        }
    }
    foreach my $w (reverse @A){
        if ( $s eq $w ) {
          $numS++;
        } else {
          last;
        }
    }
    if ( $numS % 2) {
      $oddflag = 1;
    }
}
my $i = 0;
my $b = '';
my $num = 0;
my $lastflag = 0;
foreach my $w (@A){
    if ( $i == 0 ) {
      $s = $w;
      $b = $w;
    } else {
      if ( $b eq $w ) {
        $num++;
        $b = '';
      } elsif ( $i == $numA and $s eq $w and $oddflag ) {
      } elsif ( $i == $numA and $s eq $w ) {
        $num++;
        $lastflag = 1;
      } else {
        $b = $w;
      }
    }
    $i++
}
if ( $i == 1 ) {
  print $N-1;
} else {
  my $v = $num*$N;
  $v-- if ($lastflag);
  print $v;
}