Problem:
Score : 400 points

Problem Statement

N people are arranged in a row from left to right.

You are given a string S of length N consisting of 0 and 1, and a positive integer K.

The i-th person from the left is standing on feet if the i-th character of S is 0, and standing on hands if that character is 1.

You will give the following direction at most K times (possibly zero):

Direction: Choose integers l and r satisfying 1 \leq l \leq r \leq N, and flip the l-th, (l+1)-th, ..., and r-th persons. That is, for each i = l, l+1, ..., r, the i-th person from the left now stands on hands if he/she was standing on feet, and stands on feet if he/she was standing on hands.

Find the maximum possible number of consecutive people standing on hands after at most K directions.

Constraints

N is an integer satisfying 1 \leq N \leq 10^5.

K is an integer satisfying 1 \leq K \leq 10^5.

The length of the string S is N.

Each character of the string S is 0 or 1.

Input

Input is given from Standard Input in the following format:

N K
S

Output

Print the maximum possible number of consecutive people standing on hands after at most K directions.

Sample Input 1

5 1
00010

Sample Output 1

4

We can have four consecutive people standing on hands, which is the maximum result, by giving the following direction:

Give the direction with l = 1, r = 3, which flips the first, second and third persons from the left.

Sample Input 2

14 2
11101010110011

Sample Output 2

8

Sample Input 3

1 1
1

Sample Output 3

1

No directions are necessary.

Solution in C# (Mono 4.6.2.0) (judge verdict: Accepted)

using System;
using System.Collections.Generic;
public class ABC124D {
    public static void Main() {
        int N, K, ans = 0, blockAns = 0;
        List<int> List0 = new List<int>(), List1 = new List<int>();
        string[] str = System.Console.ReadLine().Split(' ');
        N = int.Parse(str[0]);
        K = int.Parse(str[1]);
        string Sstr = System.Console.ReadLine();
        int strLeng = 0;
        bool startIs0 = Sstr[0] == '0', endIs0 = Sstr[Sstr.Length - 1] == '0';
        bool was0 = startIs0;
        for (int i = 0; i < Sstr.Length; i++) {
            if (Sstr[i] == '0') {
                if (was0) {
                    strLeng++;
                } else {
                    was0 = true;
                    List1.Add(strLeng);
                    strLeng = 1;
                }
            } else {
                if (!was0) {
                    strLeng++;
                } else {
                    was0 = false;
                    List0.Add(strLeng);
                    strLeng = 1;
                }
            }
        }
        if (was0) List0.Add(strLeng);
        else List1.Add(strLeng);
        if (startIs0) {
            for (int j0 = 0; j0 < K; j0++) {
                if (j0 < List0.Count) blockAns += List0[j0];
            }
            for (int j1 = 0; j1 < K; j1++) {
                if (j1 < List1.Count) blockAns += List1[j1];
            }
            ans = blockAns;

            // start1 = 0
            if (K < List0.Count && K < List1.Count) blockAns += -List0[0] + List0[K] + List1[K];
            if (ans < blockAns) ans = blockAns;

            for (int start1 = 1; start1 < List1.Count - K; start1++) {
                blockAns += -List1[start1 - 1] - List0[start1] + List1[start1 + K] + List0[start1 + K];
                if (ans < blockAns) ans = blockAns;
            }
            if (endIs0 && List1.Count >= K + 1) {
                blockAns += -List1[List1.Count - K - 1] - List0[List1.Count - K] + List0[List1.Count];
                if (ans < blockAns) ans = blockAns;
            } else if (endIs0 && List1.Count == 1) {
                blockAns += -List0[0] + List0[1];
                if (ans < blockAns) ans = blockAns;
            }
        } else {
            // start1 = 0
            for (int j0 = 0; j0 < K; j0++) {
                if (j0 < List0.Count) blockAns += List0[j0];
            }
            for (int j1 = 0; j1 < K + 1; j1++) {
                if (j1 < List1.Count) blockAns += List1[j1];
            }
            ans = blockAns;

            for (int start1 = 1; start1 < List1.Count - K; start1++) {
                blockAns += -List1[start1 - 1] - List0[start1 - 1] + List1[start1 + K] + List0[start1 - 1 + K];
                if (ans < blockAns) ans = blockAns;
            }
            if (endIs0 && List1.Count >= K + 1) {
                blockAns += -List1[List1.Count - K - 1] - List0[List1.Count - K - 1] + List0[List1.Count - 1];
                if (ans < blockAns) ans = blockAns;
            }
        }
        System.Console.WriteLine(ans);
    }
}