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.

Examples

Input

issii
2

Output

4

Input

qq
81

Output

81

Input

cooooooooonteeeeeeeeeest
999993333

Output

8999939997

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