Longest Subsegment with At Most K Distinct Characters

You are given a string s and an integer K. Your task is to find the length of the longest contiguous subsegment (substring) of s that contains at most K distinct characters.

More formally, if you denote the substring by s[i...j] (where 0 \le i \le j < n and n is the length of s), you need to maximize j - i + 1 subject to the condition that the number of distinct characters in s[i...j] is at most K.

You can represent the condition mathematically as:

$$\text{max length} = \max_{0 \le i \le j < n} \{ j - i + 1 \mid |\{s[i], s[i+1], \ldots, s[j]\}| \le K \} $$

If K = 0 or the string is empty, the answer is 0.

inputFormat

The input is given via standard input (stdin) and consists of two lines:

• The first line contains the string s.
• The second line contains an integer K, which represents the maximum number of distinct characters allowed.

outputFormat

Output a single integer to standard output (stdout) which is the length of the longest contiguous subsegment of s that contains at most K distinct characters.

## sample

abcba
2

3