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 Lua (5.3.2) (judge verdict: Accepted)

local s=io.read()
local k=io.read("n")

local t={}
for i=1,#s do
    t[i]=s:sub(i,i)
end

local a=0
local b=0
if t[1]==t[#s] then
    for i=1,#s do
        a=a+1
        if t[i]~=t[i+1] then
            break
        end
    end
    for i=#s,1,-1 do
        b=b+1
        if t[i]~=t[i-1] then
            break
        end
    end
end

local c=0
for i=1,#s-1 do
    if t[i]==t[i+1] then
        t[i+1]=0
        c=c+1
    end
end

if a==#s then
    print(#s*k//2)
elseif a==0 then
    print(c*k)
else
    print(c*k-(a//2+b//2-(a+b)//2)*(k-1))
end