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 AGC39_A
  character(100)::S
  integer(8)::i,J=1,K,L(100)=1,M(100)=1,N
  read(*,*)S
  read(*,*)K
  N=len_trim(S)
  do i=1,N-1
     if(S(i:i)==S(i+1:i+1)) then
        L(J)=L(J)+1
     else
        J=J+1
     end if
  end do
  if(S(1:1)/=S(N:N)) then
     L=L/2
     write(*,*)sum(L)*K
  else
     M=L
     if(J/=1) then
        M(J)=M(J)+M(1)
        M(1)=0
        M=M/2
        L=L/2
        write(*,*)L(1)+sum(M)*K-M(J)+L(J)
     else
        write(*,*)M(1)*K/2
     end if
  end if
end program AGC39_A