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;



namespace CSharpSample01
{

    

    class Program
    {
        
        static void Solve(string S, int K)
        {

            //1 or 0 のかたまりの個数が入っている
            //1010 or 0101のような10の順除(最初が1か0かによる)
            List<int> one_zero = new List<int>();
            List<int> val = new List<int>();

            bool zero = false;
            if (S[0] == '0')
            {
                zero = true;
            }
            int cnt = 0;
            for (int i = 0; i < S.Length; i++)
            {
                if (zero)
                {
                    if (S[i] == '0')
                    {
                        cnt++;
                    }
                    else
                    {
                        zero = false;
                        one_zero.Add(cnt);
                        val.Add(0);
                        cnt = 1;
                    }
                }
                else
                {
                    if (S[i] == '1')
                    {
                        cnt++;
                    }
                    else
                    {
                        zero = true;
                        one_zero.Add(cnt);
                        val.Add(1);
                        cnt = 1;
                    }
                }
            }

            one_zero.Add(cnt);
            if (zero) val.Add(0);
            else val.Add(1);
            
            int ans = 0;
            //l:範囲左端 r:範囲右端
            int l = 0;
            int r = 0;
            cnt = 0;
            //最初の範囲を求める
            //ansの初期状態を求める
            for(int i = 0; i < one_zero.Count; i++)
            {
                ans += one_zero[i];
                r = i;
                if (val[i] == 0) cnt++;

                if (cnt == K)
                {
                    if (i + 1 < one_zero.Count) ans += one_zero[i + 1];
                    r = i + 1;
                    break;
                }
            }
            
            //範囲(l, r)をずらしながらansを更新
            int next = ans;

            //Console.WriteLine($"l:{l} r:{r} next:{next}");

            while (r != one_zero.Count - 1)
            {

                l++;
                r++;
                next = next - one_zero[l - 1] + one_zero[r];

                if(val[l] != 1)
                {
                    l++;
                    next -= one_zero[l - 1];
                }
                if(val[r] != 1)
                {
                    if(r != one_zero.Count - 1)
                    {
                        r++;
                        next += one_zero[r];
                    }
                }

                //Console.WriteLine($"l:{l} r:{r} next:{next}");

                ans = Math.Max(ans, next);

            }

            Console.WriteLine(ans);
            
        }

        static void Main(string[] args)
        {
            string[] input = Console.ReadLine().Split(' ');
            int N = int.Parse(input[0]);
            int K = int.Parse(input[1]);
            string S = Console.ReadLine();

            Solve(S, K);
        }
    }

}