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

namespace d
{
    class Program
    {
        static void Main(string[] args)
        {
            int n, k;
            {
                var si = Console.ReadLine().Split(' ');
                n = int.Parse(si[0]);
                k = int.Parse(si[1]);
            }
            string s = Console.ReadLine();

            List<int> ones = new List<int>();
            List<int> zeros = new List<int>();

            bool readingOne = true;
            if (s[0] == '0')
            {
                readingOne = false;
                ones.Add(0);
            }

            int index = 0;
            while (index < s.Length)
            {
                int start = index;
                while (index < s.Length && ((readingOne && s[index] == '1') || (!readingOne && s[index] == '0')))
                    index++;
                // index will be next index
                int cnt = index - start;
                if (readingOne)
                {
                    ones.Add(cnt);
                } else
                {
                    zeros.Add(cnt);
                } 
                readingOne = !readingOne;
            }

            if (readingOne)
                ones.Add(0);

            while (zeros.Count < k)
            {
                ones.Add(0);
                zeros.Add(0);
            }

            Debug.Assert(ones.Count == zeros.Count + 1);

            int ret = 0;
            int cur = 0;
            for (int i = 0; i < k; i++)
            {
                cur += ones[i];
                cur += zeros[i];
            }
            cur += ones[k];

            ret = cur;
            for (int i = 0; i + k < zeros.Count; i++)
            {
                cur -= ones[i];
                cur -= zeros[i];

                cur += ones[i + k + 1];
                cur += zeros[i + k];
                ret = Math.Max(ret, cur);
            }

            Console.WriteLine("{0}", ret);
        }
    }
}