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 static System.Console;


class Program
{
    static void Main()
    {
        int n, k;
        var t = ReadIntArray();
        n = t[0]; k = t[1];
        
        string s;
        s = ReadLine();
        int len = s.Length;
        s = s + "E" ; // sentinel

        int l = 0, r = 0;

        // skip '1's
        while (s[r] == '1'){ r++; }
        for (int i = 0; i < k; i++){
            // skip '0's
            while (s[r] == '0'){ r++; }
            // skip '1's
            while (s[r] == '1'){ r++; }
        }
 
        int ans = r - l;
  
        while (r < len){
            // NEXT L
            // skip '1's
            while (s[l] == '1'){ l++; }
            // skip '0's
            while (s[l] == '0'){ l++; }
 
            // NEXT R
            // skip '0's
            while (s[r] == '0'){ r++; }
            // skip '1's
            while (s[r] == '1'){ r++; }
 
            ans = Math.Max(ans, r - l);
        }

        WriteLine(ans);
    }

    static int[] ReadIntArray()
    {
        return ReadLine().Split().Select(x => int.Parse(x)).ToArray();
    }
}