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)

edist' :: Char -> String -> (Int, Bool)
edist' h (x:[]) = (0, h == x)
edist' h (x:x':[])
	| x == x'   = (1, False)
	| otherwise = (0, False)
edist' h (x:x':xs)
	| x == x'   = let (n, l) = edist' h xs in (n + 1, l)
	| otherwise = edist' h (x':xs)

looped xs = head xs == last xs

edist :: String -> Int -> Int
edist xs k = k * n + if l then k - 1 else 0
	where (n, l) = edist' (head xs) xs

main :: IO ()
main = do
	xs <- getLine
	k <- readLn
	print $ edist xs k