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: Wrong Answer)

let s = read_line ()
let k = Scanf.sscanf (read_line ()) "%d" @@ fun k -> k

let s_len = String.length s

let f () = 
  let change = Array.make s_len 0 in
  for i = 1 to s_len - 1 do
    if s.[i] = s.[i - 1] && change.(i - 1) = 0 then change.(i) <- 1
  done;
  Array.fold_left (+) 0 change * k + if s.[0] = s.[s_len - 1]  && change.(s_len - 1) = 0 then k - 1  else 0

let () =
  Printf.printf "%d\n" @@ match s_len with
    | 1 -> k / 2
    | 2 -> if s.[0] = s.[1] then k else 0
    | _ -> f ()