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 Julia (0.5.0) (judge verdict: Runtime Error)

c = strip(readline())
l = parse(Int, strip(readline()))
if c[1] != c[end]
  c = c * "#"
  dl = 1
  res = 0
  for i in 2:length(c)
    if c[i] != c[i-1]
      res += div(dl, 2) * l
      dl = 1
    else
      dl += 1
    end
  end
  println(res)
elseif length(Set(collect(c))) == 1
  println(div(len(c) * l, 2))
else
  dlus = Int64[]
  c = c * "#"
  dl = 1
  res = 0
  for i in 2:length(c)
    if c[i] != c[i-1]
      push!(dlus, dl)
      dl = 1
    else
      dl += 1
    end
  end
  for i in dlus[2:end-1]
    res += div(i, 2) * l
  end
  res += div(dlus[1], 2)
  res += div(dlus[end], 2)
  res += div(dlus[1] + dlus[end], 2) * (l-1)
  println(res)
end