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.

issii
2

4

$T$ is issiiissii. For example, we can rewrite it into ispiqisyhi, and now any two adjacent characters are different.

qq
81

81

cooooooooonteeeeeeeeeest
999993333

8999939997