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 Ruby (2.3.3) (judge verdict: Accepted)

s = gets.chomp
k = gets.to_i
a = 0
t = s.dup
t.size.pred.times do |i|
  if t[i] == t[i + 1]
    a += 1
    t[i + 1] = '0'
  end
end
b = 0
t = s.dup * 2
t.size.pred.times do |i|
  if t[i] == t[i + 1]
    b += 1
    t[i + 1] = '0'
  end
end
c = 0
t = s.dup * 3
t.size.pred.times do |i|
  if t[i] == t[i + 1]
    c += 1
    t[i + 1] = '0'
  end
end
d = 0
t = s.dup * 4
t.size.pred.times do |i|
  if t[i] == t[i + 1]
    d += 1
    t[i + 1] = '0'
  end
end
if a == b - a
  puts a * k
elsif b - a == c - b
  puts a + (k - 1) * (b - a)
elsif a == (c - b) && (b - a) == (d - c)
  puts a * k / 2 + (b - a) * k / 2 if k.even?
  puts a * (k + 1) / 2 + (b - a) * (k - 1) / 2 if k.odd?
end