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 Common Lisp (SBCL 1.1.14) (judge verdict: Wrong Answer)

(defparameter *s* (read-line))
(defparameter *k* (read))

(setf *s* (concatenate 'string *s* *s*))

(defun hoge (s cur cum flag)
  (if (>= (1+ cur) (length s))
    cum
    (if (and (equal (char s cur) (char s (1+ cur))) flag)
      (hoge s (1+ cur) (1+ cum) nil)
      (hoge s (1+ cur) cum t))))

(defun piyo (s cur cum)
  (if (>= (1+ cur) (length s))
    cum
    (if (not (equal (char s cur) (char s (1+ cur)))) nil (piyo s (1+ cur) t))))

(if (piyo *s* 0 t)
  (format t "~a~%" (floor (/ (* *k* (length *s*)) 4)))
  (format t "~a~%" (min (floor (/ (* *k* (hoge *s* 0 0 t)) 2)) (floor (/ (* *k* (hoge (reverse *s*) 0 0 t)) 2)))))