Count 'ab' Occurrences in Repeated String

Given a string (s) and an integer (n), construct a new string by repeating (s) until its length reaches (n) (if necessary, take only the first few characters of an extra copy so that the final string has exactly (n) characters). Your task is to count the number of occurrences of the substring 'ab' in the resulting string.

Formally, if (L = |s|), then the resulting string (T) is defined as follows:
(T = s \times \left\lfloor \frac{n}{L} \right\rfloor + s[0:(n \bmod L)]).

Count how many times the pattern "ab" appears in (T).

inputFormat

The input is read from standard input. The first line contains the string (s). The second line contains the integer (n), the desired length of the repeated string.

outputFormat

Output a single integer, which is the count of occurrences of the substring "ab" in the repeated string.## sample

abab
10

5