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

namespace Atcoder
{
    public class Program
    {
        private static long mod = 1000000007;

        static void Main(string[] args)
        {
            var r = ReadSplit();
            var n = r[0].Int();
            var k = r[1].Int();
            var s = Read();
            var l = new List<int>();
            var pre = '2';
            var start = s[0].Int();
            var count = 0;
            for (int i = 0; i < n; i++)
            {
                if (pre == s[i])
                {
                    count++;
                }
                else
                {
                    if (count != 0) l.Add(count);
                    count = 1;
                    pre = s[i];
                }
                if (i == n - 1)
                {
                    l.Add(count);
                }
            }
            var ls = new int[l.Count + 1];
            for (int i = 0; i < l.Count; i++)
            {
                ls[i + 1] = ls[i] + l[i];
            }
            var ans = 0L;
            var startR = false;
            if (s[0] == '1') startR = true;
            for (int i = 0; i < ls.Length; i++)
            {
                if (i - 1 < 0) continue;
                var sub = 0;
                if (i % 2 == 0 && startR || i % 2 == 1 && !startR) sub = k * 2 - 1;
                else sub = k * 2;
                if (i + sub > ls.Length - 1)
                {
                    ans = Math.Max(ls[ls.Length - 1] - ls[i - 1], ans);
                }
                else
                {
                    ans = Math.Max(ls[i + sub] - ls[i - 1], ans);
                }
            }
            if (ans == 0)
            {
                ans = ls.Max();
            }
            WriteRead(ans);
        }
        
        public static string Read()
        {
            return Console.ReadLine();
        }

        public static string[] ReadSplit()
        {
            return Console.ReadLine().Split(' ');
        }

        public static void WriteRead(object str)
        {
            Console.WriteLine(str);
            Read();
        }

        public static void Write(object str)
        {
            Console.WriteLine(str);
        }

        private static bool ChangeMin<T>(ref T a, T b) where T : IComparable
        {
            if (a.CompareTo(b) > 0)
            {
                a = b;
                return true;
            }
            return false;
        }

        private static bool ChangekMax<T>(ref T a, T b) where T : IComparable
        {
            if (b.CompareTo(a) > 0)
            {
                a = b;
                return true;
            }
            return false;
        }
    }
}


public static class Extentions
{
    public static int Int(this object obj)
    {
        return int.Parse(obj.ToString());
    }

    public static long Long(this object obj)
    {
        return long.Parse(obj.ToString());
    }

    public static decimal Decimal(this object obj)
    {
        return decimal.Parse(obj.ToString());
    }

    public static double Double(this object obj)
    {
        return double.Parse(obj.ToString());
    }

    public static T2 GetValueZero<T1, T2>(this Dictionary<T1, T2> d, T1 key) where T2 : struct
    {
        T2 value;
        if (d.TryGetValue(key, out value))
        {
            return value;
        }
        return new T2();
    }
}