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 Rust (1.15.1) (judge verdict: Wrong Answer)

use std::io::prelude::*;
use std::io::stdin;
use std::str::FromStr;

fn main() {
    let s = read::<String>().as_bytes().to_vec();
    let k: u64 = read();

    let mut count = 1;
    let mut v = vec![];

    for sub in s.windows(2) {
        if sub[0] == sub[1] {
            count += 1;
        } else {
            v.push(count);
            count = 1;
        }
    }
    v.push(count);

    let ans: u64 = if v.len() == 1 {
        v[0] * k / 2
    } else if s[..].last() == s[..].first() {
        let first = *v.first().unwrap();
        let last = *v.last().unwrap();
        let mid: u64 = v[1..v.len() - 2].iter().sum();
        (first + last) / 2 * (k - 1) + mid * k + first / 2 + last / 2
    } else {
        v.iter().map(|x| x / 2).sum::<u64>() * k
    };

    println!("{}", ans);
}

#[allow(dead_code)]
fn read<T: FromStr>() -> T {
    let stdin = stdin();
    let token: String = stdin
        .lock()
        .bytes()
        .map(|b| b.unwrap() as char)
        .skip_while(|c| c.is_whitespace())
        .take_while(|c| !c.is_whitespace())
        .collect();
    token.parse().ok().unwrap()
}