Connection and Disconnection

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

inputFormat

Input

Input is given from Standard Input in the following format:

S K

outputFormat

Output

Print the minimum number of operations required.

Examples

Input

issii 2

Output

4

Input

qq 81

Output

81

Input

cooooooooonteeeeeeeeeest 999993333

Output

8999939997

样例

cooooooooonteeeeeeeeeest
999993333

8999939997