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 Kotlin (1.0.0) (judge verdict: Accepted)


fun num(input: String) : Long {
    var i = 0L
    var r = 0L
    var prev = ' '
    input.forEach {
        if (prev != it) {
            r += i / 2
            i = 1
        } else {
            i++
        }
        prev = it
    }
    r += i / 2
    return r
}

fun main(args: Array<String>) {
    val input = readLine()!!
    val k = readLine()!!.toLong()

    val one = num(input)
    val two = num(input.repeat(2))

    val allSame = input.all { it == input.first() }
    if (allSame) {
        println(input.length * k / 2)
    } else {
        println((two - one) * (k - 1) + one)
    }
}