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 connection_and_disconnection
  implicit none
  character(100) :: s
  integer :: n, i, x(100) = 0, y(100) = 0
  integer(8) :: k, a1 = 0_8, a2 = 0_8
  read(*,*) s
  read(*,*) k
  n = len_trim(s)
  do i = 1, n
    x(i) = ichar(s(i:i))-96
    y(i) = x(i)
  end do
  do i = 2, n
    if (x(i) == x(i-1)) then
      x(i) = 100
      a1 = a1+1_8
    end if
  end do
  a1 = k*a1
  if (x(n) == x(1)) a1 = a1+k-1_8
  do i = n-1, 1, -1
    if (y(i) == y(i+1)) then
      y(i) = 100
      a2 = a2+1_8
    end if
  end do
  a2 = k*a2
  if (y(1) == y(n)) a2 = a2+k-1_8
  write(*,'(i0)') min(a1,a2)
end program connection_and_disconnection