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)

Scanf.scanf "%s %d" (fun s k ->
    let n = String.length s in
    let check p s =
        let rec loop i p acc =
            if i = n then acc, p else
                if s.[i] = p then loop (i + 1) '@' (acc + 1) else
                                  loop (i + 1) s.[i] acc
        in
        loop 0 p 0
    in
    let a1, p = check '@' s in
    let a2, p = check p   s in
    let a3, _ = check p   s in
    let k2 = (k - 1) / 2 in
    let k1 = (k - 1) - k2 in
    Printf.printf "%d\n" @@ a1 + a2 * k1 + a3 * k2
)