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.Linq;
using System.Collections.Generic;
using static System.Console;
using System.Text;
using System.IO;
using static System.Math;
namespace AtCoder
{
    class Program
    {
        static public long[] Sarray() { return ReadLine().Split().Select(long.Parse).ToArray(); }
        static public List<long> Slist() { return ReadLine().Split().Select(long.Parse).ToList(); }
        static long Mod = (long)1e9 + 7;
        static void Main(string[] args)
        {
            //SetOut(new StreamWriter(OpenStandardOutput()) { AutoFlush = false });
            var NK = Sarray();
            var N = NK[0];
            var K = NK[1];
            var S = ReadLine();
            var runlen = new List<Tuple<char, long>>();
            for (var i = 0; i < N; ++i)
            {
                var t = S[i];
                var cnt = 1L;
                while (i < N - 1 && t == S[i + 1])
                {
                    ++cnt;
                    ++i;
                }
                runlen.Add(Tuple.Create(t, cnt));
            }
            //最初の塊が直立の場合
            var rui = new long[runlen.Count + 1];
            for (var i = 1; i < rui.Length; ++i)
                rui[i] = rui[i - 1] + runlen[i - 1].Item2;
            var ans = 0L;
            var strt = 0L;
            if (runlen[0].Item1 == '0')
            {
                var l = Min(runlen.Count, K * 2);
                ans = rui[l];
                strt = 1;
            }
            for (var i = strt; i < runlen.Count; i += 2)
            {
                var l = Min(runlen.Count, i + K * 2 + 1);
                ans = Max(ans, rui[l] - rui[i]);
            }
            WriteLine(ans);
            //Out.Flush();
        }
    }
}