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 Python (3.4.3) (judge verdict: Wrong Answer)

# coding: utf-8
from decimal import *
S = input()
K = Decimal(input())
if len(S) == 1:#文字列の長さが1のときは話が変わる
    ans = K // 2
    print(ans)
    exit()
fletter = 0 # 最初の文字の連続数を数える
lletter = 0 # 最後の文字の連続数を数える
cletter = 0 # 現在連続している文字の連続数を数える
cng = 0 # 文字変更の必要がある文字をカウント
for i in range(len(S)): # 最初の文字の連続数を数える
    if S[0] == S[i]:
        fletter += 1
    else:
        break
for i in range(len(S)):
    if S[-1] == S[-(i + 1)]:
        lletter += 1
    else:
        break
for i in range(len(S) - 1): # 1文字ずつ連続しているかを判定
    if S[i] == S[i + 1]:
        cletter += 1
    else:
        cng -= - cletter // 2
        cletter = 0
cng -= - cletter // 2 # 最終文字まで到達したら文字変更数の処理
if S[0] == S[-1] and fletter % 2 == 1 and lletter % 2 == 1:
    ans = Decimal((cng + 1) * K - 1)
else:
    ans = Decimal(cng * K)
print(ans) #解答の出力