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 C# (Mono 4.6.2.0) (judge verdict: Accepted)

using System;
using System.Linq;
using System.Collections.Generic;

namespace Algorithm
{
    class Program
    {
        static void Main(string[] args)
        {
            var s = Console.ReadLine();
            var k = long.Parse(Console.ReadLine());

            if (s.Length == 1 && k == 1)
            {
                Console.WriteLine(0);
                return;
            }

            var index = 0;
            var arr = new int[s.Length];
            arr[0] = 1;
            
            for (var i = 1; i < s.Length; i++)
            {
                if (s[i] == s[i - 1])
                    arr[index]++;
                else
                {
                    index++;
                    arr[index]++;
                }
            }

            var add = 0;
            if (s[0] == s[s.Length - 1])
                add = arr[0] / 2 +  arr[index] / 2 - (arr[0] + arr[index]) / 2;

            var count = 0L;
            for (var i = 0; i <= index; i++)
            {
                if (arr[i] == 1) continue;
                count += arr[i] / 2;
            }

            if (index == 0)
                Console.WriteLine(s.Length * k / 2);
            else
                Console.WriteLine(k * count - add * (k - 1));
        }
    }
}