PEG Judge - CCC13 Stage 2

2013 Canadian Computing Competition, Stage 2

Day 2, Problem 3: Repetitivity

Any string of length n has 2ⁿ subsequences, which are the strings obtained by deleting some subset of the characters. But these subsequences may not all be distinct. For example, the string zoo has only 6 distinct subsequences:

the subsequences z, oo, and zoo appear only once,
the empty subsequence appears only once,
and the subsequences o and zo each appear twice.

Suppose a string S has k distinct subsequences, and that the ith one appears f_i times. Then the repetitivity of S is defined as $\sum_{i=1}^{k} f_{i}^{2}$ . For example, the repetitivity of zoo is

1² + 1² + 1² + 1² + 2² + 2² = 12.

Input

Each test case contains a line containing the string S (with length at most 10000), followed by a line containing a single integer M (2 ≤ M ≤ 10⁹). You may assume that S only contains characters with ASCII codes between 33 and 126 inclusive (these are all printable, nonwhitespace characters).

For test cases worth 20% of the points, you may assume that S will be at most 20 characters long.