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: Time Limit Exceeded)

using System;
using System.Linq;
using System.Collections;
using System.Collections.Generic;

namespace AtCoder124
{
    class Program
    {
        public static void Main(string[] args)
        {
            string[] s = Console.ReadLine().Split(' ');
            int N = int.Parse(s[0]);
            int K = int.Parse(s[1]);
            string S = Console.ReadLine();
            int ressize = 0;
            int[] resblacks = new int[100001];
            int[] black = new int[100001];
            int[] white = new int[100001];
            int blackcount = 0;
            int whitecount = 0;
            int startidx = 0;
            int finishidx = 0;
            char bef = S[0];
            if (S[0] == '0')
            {
                black[blackcount] = 0;
                resblacks[blackcount] = 0;
                blackcount++;
            }
            for (int i = 0; i < N; i++)
            {
                if (S[i] == bef)
                {
                    finishidx = i;
                }
                else
                {
                    if (bef == '0')
                    {
                        white[whitecount] = finishidx - startidx + 1;
                        whitecount++;
                    }
                    else
                    {
                        black[blackcount] = finishidx - startidx + 1;
                        resblacks[blackcount] = finishidx - startidx + 1;
                        blackcount++;
                    }
                    startidx = i;
                    finishidx = i;
                    bef = S[i];
                }
            }
            if (bef == '0')
            {
                white[whitecount] = finishidx - startidx + 1;
                whitecount++;
                black[blackcount] = 0;
                resblacks[blackcount] = 0;
                blackcount++;
            }
            else
            {
                black[blackcount] = finishidx - startidx + 1;
                resblacks[blackcount] = finishidx - startidx + 1;
                blackcount++;
            }
            ressize = blackcount;
            int res = resblacks[0];
            for (int i = 0; i < K; i++)
            {
                if (ressize == 1) break;
                if (whitecount == 0) break;
                for (int j = 0; j < ressize - 1; j++)
                {
                    resblacks[j] = resblacks[j] + black[j + i + 1] + white[j + i];;
                    res = Math.Max(res, resblacks[j]);
                }
                ressize--;
            }
            Console.WriteLine(res);
        }
    }
}