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 static Exter;
using System.Linq;
#if DEBUG
#else
using console = System.Console;
#endif

public class App
{
    public static void Main(string[] args)
    {
        var k = readarr[1];
        var e = console.ReadLine().Select(c=>c=='1');
        e=new bool[]{!e.First()}.Concat(e);
        var tmp = 1;
        var f = e.Zip(e.Skip(1),(a,b)=>new{v=b,b=(a!=b)}).Select(v=>new{v.v,cond=(v.b?tmp=1:++tmp)}).ToList();
        f.Add(new {v=!f.Last().v,cond=0});
        var g = f.Zip(f.Skip(1),(a,b)=>new{v=a.v,b=(a.v!=b.v),cond=a.cond}).Where(v=>v.b).Select(v=>new{v.cond,v.v}).ToList();
        if(g.First().v==false)
        g.Insert(0,new {cond=0,v=true});
        if(g.Last().v==false)
        g.Add(new {cond=0,v=true});
        var h = g.Select(v=>v.cond).ToArray();
        //cout = string.Join(",",h);
        if(h.Length/2<=k)
            cout = h.Sum().ToString();
        else
        {
            int max = 0;
            for(int i = 0;i<=h.Length-k*2;i+=2)
            {
                int aggregate = 0;
                for(int j = i;j<=i+k*2;j++)
                {
                    aggregate += h[j];
                }
                if(aggregate>max)
                    max = aggregate;
            }
            cout = max.ToString();
        }
    }
}
public static class Exter
{
    public static int Max(params int[] p)=>p.Max();
    public static long Max(params long[] p)=>p.Max();
    public static int Min(params int[] p)=>p.Min();
    public static long Min(params long[] p)=>p.Min();
    public static string cout
    {
        set
        {
            console.Write(value);
            console.WriteLine();
            
        }
    }
    public static int[] readarr
    {
        get 
        {
            return console.ReadLine().Split().Select(s=>int.Parse(s)).ToArray();
        }
    }
}


#if DEBUG
public static class console
{
    static int cursorLine = 0;
    static readonly string[] cin = new string[]
    {
                "14 1",
                "11111"
    };
    static public string ReadLine()
    { 
        return cin[cursorLine++];
    }
    static public void WriteLine()
    {
        Console.WriteLine();
    }
    static public void WriteLine<T>(T input)
    {
        Console.WriteLine(input);
    }
    static public void Write<T>(T input)
    {
        Console.Write(input);
    }
    static public void WriteLine(string s,params object[] arr)
    {
        Console.WriteLine(s,arr);
    }
}
#endif