Count the 'a's in an Infinite Repeating String

You are given a string s and an integer n. Consider an infinite string formed by repeating s indefinitely. Your task is to calculate the number of occurrences of the character a in the first n characters of this infinite string.

Formally, let T be the infinite string defined as:

\(T = s s s \cdots\)

You need to determine the number \(k\) such that \(k\) is the total number of occurrences of a in the first n characters of T.

Note: The value of n can be extremely large, so your solution must be efficient.

inputFormat

The input is read from stdin and consists of two lines:

• The first line contains the string s.
• The second line contains the integer n, representing the number of characters to consider.

outputFormat

Output a single integer to stdout representing the number of times the letter a appears in the first n characters of the infinite repeated string.

abcac
10

4