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: Accepted)

program name
    use,intrinsic :: iso_fortran_env
    implicit none
    integer(int64):: k,i,n,a1,a2
    character(100):: s
    character(200):: s2
    logical:: one_word = .true.

    read*, s
    read*, k
    n = len_trim(s)
    do i=1,n
        if (s(1:1) /= s(i:i)) one_word = .false.
    end do

    if (one_word) then
        print'(i0)', (n*k)/2
        stop
    end if

    s2 = trim(s) // trim(s)

    a1 = serch(s,n)
    a2 = serch(s2,2*n)

    print'(i0)', a1*k + (a2-2*a1)*(k-1)

contains
    function serch(str,n) result(ret)
        character(*):: str
        integer(int64):: n,ret
        integer(int64):: i

        ret = 0
        do i=2,n
            if (str(i:i) == str(i-1:i-1)) then
                ret=ret+1
                str(i:i)='0'
            end if
        end do
    end function
end program name