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;
using System.Linq;
using System.Text;
using System.Threading.Tasks;

namespace Beg124D
{
    class Program
    {
        public static int N;
        static void Main(string[] args)
        {
            var read = Console.ReadLine().Split(' ').Select(x => int.Parse(x)).ToArray();
            N = read[0];
            var K = read[1];

            var S = Console.ReadLine().ToArray();
            var start1 = S[0] == '1';
            var end1 = S[S.Length - 1] == '1';
            var S_Count = new List<int>();
            var count = 1;

            if (S.Length == 1)
            {
                Console.WriteLine(K > 0 ? 1 : 0);
            }

            if (!start1) S_Count.Add(0);
            for (int i = 0; i < S.Length - 1; i++)
            {
                if (S[i] == '0' && S[i + 1] == '1')
                {
                    S_Count.Add(-count);
                    count = 1;
                    if (i == S.Length - 2) S_Count.Add(1);
                }
                else if (S[i] == '1' && S[i + 1] == '0')
                {
                    S_Count.Add(count);
                    count = 1;
                    if (i == S.Length - 2) S_Count.Add(-1);
                }
                else
                {
                    count++;
                    if (i == S.Length - 2) S_Count.Add(S[i] == '1' ? count : -count);
                }
            }
            if (!end1) S_Count.Add(0);

            var ret = new List<int>();


            S_Count = S_Count.Select(x => Math.Abs(x)).ToList();
            var beginTarget = 0;
            var endTarget = 2 * K + 1 - 1;
            var sumNum = S_Count.Where((x, i) => i <= endTarget).Sum();
            ret.Add(sumNum);
            if (endTarget >= S_Count.Count() && S.Count() != 1)
                Console.WriteLine(N);
            for (int i = endTarget; i < S_Count.Count() - 2; i += 2)
            {
                sumNum -= S_Count[beginTarget] + S_Count[beginTarget + 1];
                sumNum += S_Count[endTarget + 1] + S_Count[endTarget + 2];
                beginTarget += 2;
                endTarget += 2;
                ret.Add(sumNum);
            }

            if(endTarget < S_Count.Count() && S.Count() != 1) Console.WriteLine(ret.Max());

        }
        public static int MaxHandStandNum(int K, List<int> S_Count, int preIndex)
        {
            if (K == 0)
                return S_Count.Max();
            else if (S_Count.Count() == 1)
                return Math.Max(S_Count[0], 1);

            var ret = new List<int>();
            var tempS_Count = new List<int>(S_Count);
            if (preIndex == 0)
            {
                var combine = tempS_Count[0] - tempS_Count[1];
                tempS_Count[0] = combine;
                tempS_Count.RemoveAt(1);
                return MaxHandStandNum(K - 1, tempS_Count, 0);
            }
            else if (preIndex == S_Count.Count() - 1)
            {
                var combine = -tempS_Count[S_Count.Count() - 2] + tempS_Count[S_Count.Count() - 1];
                tempS_Count[preIndex] = combine;
                tempS_Count.RemoveAt(preIndex - 1);
                return MaxHandStandNum(K - 1, tempS_Count, preIndex - 1);
            }
            else
            {
                var combine = tempS_Count[preIndex - 2] - tempS_Count[preIndex - 1] + tempS_Count[preIndex];
                tempS_Count[preIndex - 2] = combine;
                tempS_Count.RemoveAt(preIndex);
                tempS_Count.RemoveAt(preIndex - 1);
                ret.Add(MaxHandStandNum(K - 1, tempS_Count, preIndex - 2));

                tempS_Count = new List<int>(S_Count);
                combine = tempS_Count[preIndex] - tempS_Count[preIndex + 1] + tempS_Count[preIndex + 2];
                tempS_Count[preIndex] = combine;
                tempS_Count.RemoveAt(preIndex + 2);
                tempS_Count.RemoveAt(preIndex + 1);
                ret.Add(MaxHandStandNum(K - 1, tempS_Count, preIndex));

                return ret.Max();
            }

        }

        public static int MaxHandStandNum(int K, List<int> S_Count)
        {
            if (K == 0)
                return S_Count.Max();
            else if (S_Count.Count() == 1)
                return Math.Max(S_Count[0], 1);

            var ret = new List<int>();
            var tempS_Count = new List<int>();
            for (int i = 0; i < S_Count.Count(); i++)
            {
                if (S_Count[i] < 0)
                {
                    tempS_Count = new List<int>(S_Count);
                    if (i == 0)
                    {
                        var combine = -tempS_Count[0] + tempS_Count[1];
                        tempS_Count[0] = combine;
                        tempS_Count.RemoveAt(1);
                        ret.Add(MaxHandStandNum(K - 1, tempS_Count));
                    }
                    else if (i == S_Count.Count() - 1)
                    {
                        var combine = tempS_Count[i - 1] - tempS_Count[i];
                        tempS_Count[i - 1] = combine;
                        tempS_Count.RemoveAt(i);
                        ret.Add(MaxHandStandNum(K - 1, tempS_Count));
                    }
                    else
                    {
                        var combine = S_Count[i - 1] - S_Count[i] + S_Count[i + 1];
                        tempS_Count[i] = combine;
                        tempS_Count.RemoveAt(i + 1);
                        tempS_Count.RemoveAt(i - 1);
                        ret.Add(MaxHandStandNum(K - 1, tempS_Count));

                    }
                }
            }

            return ret.Max();

        }
    }
}