Longest Substring 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 substring of s that contains at most k distinct characters.

More formally, let a substring s[i...j] be valid if it contains at most k distinct characters. You need to compute the value:

\(\max_{0 \leq i \leq j < n}\{j - i + 1 \mid s[i...j] \text{ contains at most } k \text{ distinct characters}\}\)

where n is the length of the string. It is guaranteed that the string consists only of lowercase English letters.

inputFormat

The input is given on two lines:
The first line contains a non-negative string s consisting of lowercase alphabets.
The second line contains an integer k denoting the maximum number of distinct characters allowed.

outputFormat

Print the length of the longest substring of s that contains at most k distinct characters to standard output.

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