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 string InputPattern = "InputX";

    static List<string> GetInputList()
    {
        var WillReturn = new List<string>();

        if (InputPattern == "Input1") {
            WillReturn.Add("5 1");
            WillReturn.Add("00010");
            //4
        }
        else if (InputPattern == "Input2") {
            WillReturn.Add("14 2");
            WillReturn.Add("11101010110011");
            //8
        }
        else if (InputPattern == "Input3") {
            WillReturn.Add("1 1");
            WillReturn.Add("1");
            //1
        }
        else {
            string wkStr;
            while ((wkStr = Console.ReadLine()) != null) WillReturn.Add(wkStr);
        }
        return WillReturn;
    }

    static void Main()
    {
        List<string> InputList = GetInputList();

        int[] wkArr = InputList[0].Split(' ').Select(X => int.Parse(X)).ToArray();
        int K = wkArr[1];

        char[] SArr = InputList[1].ToCharArray();
        int UB = SArr.GetUpperBound(0);

        //ランレングス圧縮を行う
        //添字が偶数なら1のLength、奇数なら0のLengthを持つ、List
        var SeqList = new List<int>();
        int SeqCnt = 1;
        for (int I = 0; I <= UB; I++) {
            if (I == 0 && SArr[I] == '0') {
                SeqList.Add(0); //左端が0なら、番兵として、左端に1を追加する(lengthは0)
            }

            //連続した範囲の最後の場合
            if (I == UB || SArr[I] != SArr[I + 1]) {
                SeqList.Add(SeqCnt);
                SeqCnt = 1;
            }
            else {
                SeqCnt++;
            }

            if (I == UB && SArr[I] == '0') {
                SeqList.Add(0); //右端が0なら、番兵として、右端に1を追加する(lengthは0)
            }
        }

        //尺取法で解く
        int R = 0;
        int CurrSum = SeqList[0];
        int Answer = SeqList[0];
        UB = SeqList.Count - 1;

        //for (int I = 0; I <= UB; I++) Console.WriteLine("SeqList[{0}]={1}", I, SeqList[I]);

        for (int L = 0; L <= UB; L += 2) {
            while (R < UB && (R - L) / 2 < K) {
                CurrSum += SeqList[R + 1];
                CurrSum += SeqList[R + 2];
                R += 2;
            }

            //Console.WriteLine("始点{0},終点{1}での和={2}", L, R, CurrSum);

            Answer = Math.Max(Answer, CurrSum);
            if (L + 2 < UB) {
                CurrSum -= SeqList[L];
                CurrSum -= SeqList[L + 1];
            }
        }
        Console.WriteLine(Answer);
    }
}