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;
using ll = long long;
using P = pair<int,int>;
#define rep(i,n) for(ll i = 0; i < (ll)(n); i++)
template<class T>bool chmax(T &a, const T &b) { if (a<b) { a=b; return 1; } return 0; }
template<class T>bool chmin(T &a, const T &b) { if (b<a) { a=b; return 1; } return 0; }
const ll INF = 1LL << 60;
int main(){
    string s;
    int k;
    cin >> s >> k;
    int tot = 0;
    int se = 1;
    int n = s.size();
    int a,b;
    bool start = true;
    rep(i,n){
        if(!i) continue;
        if(s[i]==s[i-1])se++;
        else {
            if(tot==0 && start) {
                a = se;
                start = false;
            }
            tot += se/2;
            se=1;
        }
    }
    b = se;
    tot += b/2;
    ll ans = (ll)tot*k;
    if(s[0]==s[n-1]){
        ans -= (a/2 + b/2)*(k-1);
        ans += ((a+b)/2)*(k-1);
    }
    cout << ans << endl;

    return 0;
}