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 OCaml (4.02.3) (judge verdict: Accepted)

let () = Scanf.scanf "%s\n%d" @@ fun s k ->
  let s = Array.init (String.length s) (String.get s) in
  let a = Array.init 2 @@ fun i ->
    snd @@
    Array.fold_left (fun (c, (n, b)) c' ->
      (c', if b = 1 || c <> c' then (n, 0) else (n + 1, 1)))
    (s.(Array.length s - 1), (0, i)) s in
  Printf.printf "%d\n" @@
  if snd a.(1) = 1
  then k * fst a.(1)
  else if snd a.(0) = 0
  then fst a.(1) + (k - 1) * fst a.(0)
  else (k / 2) * (fst a.(0) + fst a.(1)) + (k mod 2) * fst a.(1)