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;
using static System.Console;

class Program
{
    static void Main()
    {
        var NK = ReadLine().Split().Select(int.Parse).ToArray();
        var N = NK[0];
        var K = NK[1];
        var S = ReadLine();

        var m = S[0];
        var max = 1;
        var c = S[0] == '0' ? 1 : 0;
        var s = 0;
        for (int i = 1; i < N; i++)
        {
            if (m == '1' && S[i] == '0')
            {
                c++;
                if (c > K)
                {
                    if (S[s] == '1') while (S[s] == '1') s++;
                    while (S[s] == '0') s++;
                    if (s > i) i = s;
                    c--;
                }
            }
            max = Math.Max(max, i - s + 1);
            m = S[i];
        }
        WriteLine(max);
    }
}