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;

class Program
{
    static void Main(string[] args)
    {
        var N = sc.ReadInt();
        var K = sc.ReadInt();
        var S = sc.ReadStr();
        var rle = RLE(S).ToList();
        if (rle[0].Item1 == '0')
        {
            rle.Insert(0, Tuple.Create('1', 0));
        }
        if (rle.Last().Item1 == '0')
        {
            rle.Add(Tuple.Create('1', 0));
        }
        var ans = rle.Where(t => t.Item1 == '0').Take(K).Sum(t => t.Item2);
        ans += rle.Where(t => t.Item1 == '1').Take(K + 1).Sum(t => t.Item2);
        var prev = ans;
        for (int i = 3; i < rle.Count(); i += 2)
        {
            var r1 = i - 3;
            var r0 = i - 2;
            var res = prev - rle[r1].Item2 - rle[r0].Item2;
            var p1 = i + (K - 1) * 2 + 1;
            var p0 = i + (K - 1) * 2;
            if (p1 >= rle.Count) break;
            res += rle[p0].Item2 + rle[p1].Item2;
            ans = Math.Max(ans, res);
            prev = res;
        }
        Console.WriteLine(ans);
    }

    static IEnumerable<Tuple<char, int>> RLE(string s)
    {
        var count = 1;
        var c = s[0];
        for (int i = 1; i < s.Length; i++)
        {
            if (c == s[i])
            {
                count++;
            }
            else
            {
                yield return Tuple.Create(c, count);
                count = 1;
            }
            c = s[i];
        }
        yield return Tuple.Create(c, count);
    }

    static Scanner sc = new Scanner();
}

class Scanner
{
    string[] S = new string[0];
    int Index = 0;
    char[] Separators = new char[] { ' ' };

    public string Next()
    {
        if (this.Index < this.S.Length) return this.S[this.Index++];
        var line = "";
        while (line == "") line = Console.ReadLine();
        this.S = line.Split(this.Separators, StringSplitOptions.RemoveEmptyEntries);
        if (this.S.Length == 0) return this.Next();
        this.Index = 0;
        return this.S[this.Index++];
    }
    public string ReadStr()
    {
        return this.Next();
    }
    public char ReadChar()
    {
        return this.Next()[0];
    }
    public int ReadInt()
    {
        return int.Parse(this.Next());
    }
    public uint ReadUInt()
    {
        return uint.Parse(this.Next());
    }
    public long ReadLong()
    {
        return long.Parse(this.Next());
    }
    public double ReadDouble()
    {
        return double.Parse(this.Next());
    }
    public int[] ReadIntArray(int n)
    {
        var array = new int[n];
        for (int i = 0; i < array.Length; i++)
        {
            array[i] = this.ReadInt();
        }
        return array;
    }
    public long[] ReadLongArray(int n)
    {
        var array = new long[n];
        for (int i = 0; i < array.Length; i++)
        {
            array[i] = this.ReadLong();
        }
        return array;
    }
    public double[] ReadDoubleArray(int n)
    {
        var array = new double[n];
        for (int i = 0; i < array.Length; i++)
        {
            array[i] = this.ReadDouble();
        }
        return array;
    }
    public char[] ReadCharArray(int n)
    {
        var array = new char[n];
        for (int i = 0; i < array.Length; i++)
        {
            array[i] = this.ReadChar();
        }
        return array;
    }
    public string[] ReadStrArray(int n)
    {
        var array = new string[n];
        for (int i = 0; i < array.Length; i++)
        {
            array[i] = this.ReadStr();
        }
        return array;
    }
}