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: Accepted)

S=chomp(readline())
K=parse(Int,readline())
A=Int[1]
for i=2:length(S)
	if S[i-1]==S[i]
		A[end]+=1
	else
		push!(A,1)
	end
end
if length(A)==1
	println(div(A[1]*K,2))
else
	ans=div(A[1],2)+div(A[end],2)
	T=0
	for i=2:length(A)-1
		T+=div(A[i],2)
	end
	ans+=T*K
	if S[1]==S[end]
		ans+=(K-1)*div(A[1]+A[end],2)
	else
		ans+=(K-1)*(div(A[1],2)+div(A[end],2))
	end
	println(ans)
end