Longest Contiguous Ones After Flips

Given a binary string S and an integer K, your task is to determine the maximum length of a contiguous substring consisting entirely of '1's that can be obtained by flipping at most K characters (i.e. changing '0' to '1').

You can think of the problem as finding the longest window [i, j] in the string such that the number of '0's in that window does not exceed K. Formally, you need to maximize the length $$L = j - i + 1,$$ subject to $$\sum_{t=i}^{j} \mathbf{1}_{\{S[t]=='0'\}} \le K.$$

Note that the length of the string, N, is implicitly given by len(S).

inputFormat

The input is read from standard input (stdin) and consists of two lines:

1. The first line contains the binary string S (a sequence of characters, each either '0' or '1').
2. The second line contains an integer K representing the maximum number of flips allowed.

outputFormat

Output to standard output (stdout) a single integer representing the maximum length of a contiguous substring of '1's achievable after at most K flips.

## sample

1101001100
2

5

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