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 Fortran (gfortran v4.8.4) (judge verdict: Wrong Answer)

      PROGRAM connectionAndDisconnection
      IMPLICIT NONE
      character(100) :: s
      INTEGER(16) :: k, ans
      
      INTEGER(16),allocatable :: flags(:)
      INTEGER :: len, i
      LOGICAL :: lastFlag = .false., sameFlag = .true.
      
      
      read*,s
      READ*,k
      
      len = len_trim( s )
      allocate ( flags(len) )
      flags = 0
      
      DO i = 1,len-1
        IF( s(i:i)/=s(i+1:i+1) )THEN
          sameFlag = .false.
          EXIT
        END IF
      END DO
      
      
      
      DO i = 1,len-1
        IF( s(i:i)==s(i+1:i+1) )THEN
          flags(i) = 1
          s(i+1:i+1) = 'X'
        END IF
      END DO
      !i = len
      IF( s(len:len)==s(1:1) )THEN
        flags(len) = 1
      END IF
      
      
      IF( flags(len-1)==0 )THEN
        IF( flags(len)==1 )THEN
          lastFlag = .true.
        END IF
      END IF
      
      
      ans = sum( flags(:) ) * k
      IF(lastFlag)THEN
        ans = ans -1
      END IF
      
      IF( len==1 )THEN
        IF( mod(k,2)==0 )THEN
          ans = k/2
        ELSE
          ans = (k-1)/2
        END IF
      END IF
      
      IF( sameFlag )THEN
        IF( mod(k*len,2)==0 )THEN
          ans = k*len/2
        ELSE
          ans = (k*len-1)/2
        END IF
      END IF
      print*,ans
      
      
      
      END PROGRAM