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>

int main(){
    using ll = long long;
    int K;
    std::string s;
    std::cin>>s>>K;
    ll dp[31]={};
    bool bk=true;
    for(int i=0;i+1<s.size();++i){
        if(s[i]==s[i+1]){
            dp[0]++;
            i++;
            if(i+1==s.size()) bk = false;
            if(i==0){
                bk = false;
                i--;
            }
        }
    }
    bk &= s.front()==s.back();
    ll ans=0;
    for(int i=0;i<=31;++i){
        if(i<31) dp[i+1] = 2*dp[i] + bk;
        if(K>>i&1) ans += dp[i];
    }
    std::cout<<ans<<"\n";
}