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## 문제

Diana bought a Long Random String Generator on some weird website. She planned to generate a long string s of length n and then use its contiguous substrings as passwords for other weird websites.

Soon she discovered that the generated string s of length n was not random at all, but rather a string p of length k repeated many times and then cut to length n. Thus, s[i] = p[i mod k] for all i from 0 to n − 1.

Diana wonders how many different passwords she can get from the generated string. Help her find the number of distinct non-empty substrings in string s.

## 입력

The first line of the input contains a string p consisting of k lowercase English letters (1 ≤ k ≤ 1000).

The second line contains an integer n (k ≤ n ≤ 109).

## 출력

Output the number of distinct non-empty substrings in s.

## 예제 입력 1

abba
7


## 예제 출력 1

20


## 예제 입력 2

a
42


## 예제 출력 2

42


## 노트

In the first example, the generated string is abbaabb. It contains 20 distinct non-empty substrings: a, b, aa, ab, ba, bb, aab, abb, baa, bba, aabb, abba, baab, bbaa, abbaa, baabb, bbaab, abbaab, bbaabb, abbaabb.