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: Wrong Answer)

#include <bits/stdc++.h>
using namespace std;
#define ll long long
#define all(x) x.begin(),x.end()
 
int const N = 100001;
int k;
string s; 
// a.b.a.aba.a
// aaba.a.a
// a.ba.a.aba.a.aba.a 
 
int main(){
	cin >> s >> k;
	if(s.size() == 1){cout << k/2<<"\n";return 0;}
	char x = s[0];
	int count = 0;
	for(int i = 0; i<(int)s.size(); ++i)count += (s[i] == x ? 1: 0);
	if(count == (int)s.size()){return cout << (1ll * (count/2) * k), 0;}
	if(k <= 1){
	ll an = 0;
	for(int i = 0; i<(int)s.size()-1; ++i){
	   if(s[i] == s[i+1])s[i+1] = '.', ++an;
	}
	printf("%lld\n",an);
	return 0;
    }
    string o = s;
    char c = s[s.size()-1];
    int j = 0, cc = 0;
    while(j < (int)s.size()-1 && s[j] == c)++cc,s += c, ++j;
	int d = 0, rem = 0;
	for(int i = 0; i<(int)s.size()-1; ++i){
	   if(s[i] == s[i+1]){
		  s[i+1] = '.';
	      ++d;
	      if(i >= (int)o.size()-1)++rem;
	   }
	}
	ll an = (1ll * d * k);
	an -= cc;
	printf("%lld\n",an);
}