LogiQuest

401. Task Scheduler

MediumGreedyCounting

Tasks are letters; each takes one unit of time. The same task must be separated by at least n units (idle slots allowed). Print the minimum total time.

Input format

Line 1: the tasks (uppercase letters, no spaces) Line 2: n

Output format

The minimum time.

Example 1

Input

AAABBB
2

Output

8

Example 2

Input

AAABBB
0

Output

6

Constraints

1 ≤ tasks ≤ 10⁴ 0 ≤ n ≤ 100

Read input from standard input and print the answer to standard output. Your code is judged against 4 test cases, most of them hidden.

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