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++14 (GCC 5.4.1) (judge verdict: Accepted)

#include<bits/stdc++.h>
using namespace std;

int main(){
	string s; long long k;
	cin >> s >> k;
	string t = s,d = s;
	long long ans1 = 0,ans2 = 0,ans3 = 0;
	for(int i = 1;i < s.size();i++){
		if(s[i] == s[i-1]){
			ans1++;
			s[i] = '-';
		}
	}
	t = s + t;
	for(int i = 1;i < t.size();i++){
		if(t[i] == t[i-1]){
			ans2++;
			t[i] = '-';
		}
	}
	d = t + d;
	for(int i = 1;i < d.size();i++){
		if(d[i] == d[i-1]){
			ans3++;
			d[i] = '-';
		}
	}
	long long sum = ans1 + (ans2 + ans3) * ((k-1)/2);
	if((k-1)%2 == 1) sum += ans2;
	cout << sum << endl;
	return 0;
}