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.Web;

namespace Competitive
{
    internal class Solution
    {
        public int N, K;
        public string S;
        public long MOD = 1000000007;

        public void Run()
        {
            {
                var line = Input.ReadIntArray();
                N = line[0];
                K = line[1];
            }

            S = Console.ReadLine();

            List<int> lst = new List<int>();

            {
                int last = '1';
                int i = 0;
                int c = 0;
                while (true)
                {
                    if (last != S[i])
                    {
                        lst.Add(c);
                        last = S[i];
                        c = 1;
                    }
                    else
                    {
                        c++;
                    }

                    i++;

                    if (i == N)
                    {
                        lst.Add(c);
                        if (last == '0')
                        {
                            // 1で終わるようにする
                            lst.Add(0);
                        }

                        break;
                    }
                }
            }

            // 累積和
            int[] A = new int[lst.Count];
            for (int i = 0; i < lst.Count; i++)
            {
                A[i] = i == 0 ? lst[i] : (lst[i] + A[i - 1]);
            }

            int ret = 0;
            for (int i = 0; i < lst.Count; i+=2)
            {
                int l = i;
                int r = Math.Min(lst.Count - 1, i + 2 * K);
                int sl = i == 0 ? 0 : A[i - 1];
                int sr = A[r];
                ret = Math.Max(ret, sr - sl);
            }
            Console.WriteLine(ret);
        }
    }

    // libs ----------
    

    // common ----------

    internal static class Input
    {
        public static string ReadString()
        {
            string line = Console.ReadLine();
            return line;
        }

        public static int ReadInt()
        {
            string line = Console.ReadLine();
            return int.Parse(line);
        }

        public static int[] ReadIntArray()
        {
            string line = Console.ReadLine();
            return line.Split(' ').Select(int.Parse).ToArray();            
        }

        public static long ReadLong()
        {
            string line = Console.ReadLine();
            return long.Parse(line);
        }

        public static long[] ReadLongArray()
        {
            string line = Console.ReadLine();
            return line.Split(' ').Select(long.Parse).ToArray();
        }

        public static double[] ReadDoubleArray()
        {
            string line = Console.ReadLine();
            return line.Split(' ').Select(double.Parse).ToArray();
        }
    }
    
    internal class Program
    {
        public static void Main(string[] args)
        {
            var s = new Solution();
            s.Run();
        }
    }
}