Solve the programming task below in a Python markdown code block.
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.

Examples

Input

issii
2


Output

4


Input

qq
81


Output

81


Input

cooooooooonteeeeeeeeeest
999993333


Output

8999939997