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: Runtime Error)

using System;
using System.Collections.Generic;
using System.Linq;

namespace ABC124_D
{
    class Program
    {
        static void Main(string[] args)
        {
            var NK = Console.ReadLine().Split().Select(int.Parse).ToArray();
            var N = NK[0];
            var K = NK[1];
            var S = Console.ReadLine();

            if (N == 1)
            {
                if (K >= 1 || K == 0 && S == "1")
                {
                    Console.WriteLine(1);
                    return;
                }
                else
                {
                    Console.WriteLine(0);
                    return;
                }
            }

            var list = new List<int>();
            var n = new List<char>();

            var current = S[0];
            var temp = 0;
            for (int i = 0; i < N; i++)
            {
                if (current == S[i])
                {
                    temp++;
                }
                else
                {
                    list.Add(temp);
                    n.Add(current);
                    current = S[i];
                    temp = 1;
                }
            }
            var last = N - 1;
            if (S[last] == S[last - 1])
            {
                list.Add(temp);
                n.Add(current);
            }

            var ans = 0;
            var t = 0;
            var index = 0;
            if (n[0] == '1')
            {
                t += list[0];
                index++;
            }

            for (int i = index; i < index + 2 * K; i++)
            {
                if (i == list.Count) break;
                t += list[i];
            }

            ans = Math.Max(ans, t);
            var left = 0;
            var right = 2 * K + 1;
            for (left = index; right < list.Count - 2; left += 2)
            {
                t -= list[left] + list[left + 1];
                t += list[right] + list[right + 1];
                right += 2;
                ans = Math.Max(ans, t);
            }

            last = list.Count - 1;
            if (n[last] == '0')
            {
                t -= list[left] + list[left + 1];
                t += list[right];
                ans = Math.Max(ans, t);
            }

            Console.WriteLine(ans);
        }
    }
}