Problem Statement

You are given a string $S$. Find the minimum length of a string that can be obtained by performing the following operation on the string $S$ zero or more times.

• Choose a contiguous occurrence of of in the string and an integer $i$ between $0$ and $K$, inclusive. Then, remove the of and the following $i$ characters from the string.

Constraints

• $0 \leq K < |S| \leq 300$
• $K$ is an integer.
• $S$ is a string consisting of lowercase English letters.

Input

The input is given from Standard Input in the following format:

S
K

Output

Print the answer.