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 Haskell (GHC 7.10.3) (judge verdict: Wrong Answer)

solve :: String -> Int -> Int
solve s k
  | even n    = f s * k
  | otherwise = let (d,r) = k `divMod` 2
                   in (f s * 2 + 1) * d + r * f s
  where
    n = length s
    f []  = 0
    f [_] = 0
    f (x1:x2:xs)
      | x1 == x2  = 1 + f xs
      | otherwise = f (x2:xs)

main :: IO ()
main = do
    s <- getLine
    k <- readLn :: IO Int
    print $ solve s k