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)

S = list(input())
N = len(S)
K = int(input())
  
if len(set(S)) == 1:
  print((N*K)//2)
  exit()

ans = 0
for i in range(N-1):
  if S[i] == S[i+1]:
    ans += 1
    S[i+1] = '0'

a = 0
while S[0] == S[a+1]:
  a += 1

b = 0
while S[N-1] == S[N-2-b]:
  b += 1

print(ans*K - (K-1)*(a//2 + b//2 - (a+b)//2))