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.