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 2.0.3) (judge verdict: Accepted)

(let* ((s (read-line))
       (k (read))
       (x (make-array (list (length s)) :adjustable t :fill-pointer 0)))
  ;;
  (loop :with d := #\*
        :for c :across s
        :if (char/= c d)
        :do (progn
              (vector-push-extend 1 x)
              (setf d c))
        :else
        :do (incf (aref x (1- (length x)))))
  (cond ((= (length x) 1)
         (format t "~A~%" (floor (* k (aref x 0)) 2)))
        ((char/= (aref s 0) (aref s (1- (length s))))
         (format t "~A~%" (loop :for n :across x
                                :sum (* k (floor n 2)))))
        (t
         (format t "~A~%" (+ (loop :for i :from 1 :to (- (length x) 2)
                                   :sum (* k (floor (aref x i) 2)))
                             (floor (aref x 0) 2)
                             (floor (aref x (1- (length x))) 2)
                             (* (1- k) (floor (+ (aref x 0) (aref x (1- (length x)))) 2)))))))