Counting Palindromic Strings

Eli is fascinated by palindromes—strings that read the same forwards and backwards. Given a set of characters and an integer length L, your task is to count how many palindromic strings of length L can be constructed using only the characters from the provided set.

Note that for a palindrome, only the first half (and the middle character if L is odd) determines the entire string. Mathematically, if there are m distinct characters in the set, the number of palindromes is given by:

• If L is even: \( m^{\frac{L}{2}} \)
• If L is odd: \( m^{\frac{L+1}{2}} \)

For example, if the set is abc and L = 3, the answer would be \( 3^{\frac{3+1}{2}} = 3^2 = 9 \).

Your program should read input from stdin and produce output to stdout.

inputFormat

The input consists of two values separated by whitespace:
1. A non-empty string representing the available set of characters.
2. An integer L representing the required length of the palindromic strings.

Input is read from standard input (stdin).

outputFormat

Output a single integer which is the number of palindromic strings that can be formed using the given set of characters and length. The result should be written to standard output (stdout).## sample

abc
1

3