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 D
{
	static void Main()
	{
		var h = Console.ReadLine().Split().Select(int.Parse).ToArray();
		var k = h[1];
		var s = Console.ReadLine();

		var tl = new List<int>();
		var tc = '1';
		var tn = 0;
		foreach (var c in s)
		{
			if (c != tc)
			{
				tl.Add(tn);
				tc = c;
				tn = 0;
			}
			tn++;
		}
		tl.Add(tn);
		if (tc == '0') tl.Add(0);

		var c0 = tl.Where((x, i) => i % 2 == 1).ToArray();
		var c1 = tl.Where((x, i) => i % 2 == 0).ToArray();

		int M = c0.Take(k).Sum() + c1.Take(k + 1).Sum(), t = M;
		for (int l = 0, r = k; r < c0.Length; l++, r++)
			M = Math.Max(M, t += c0[r] + c1[r + 1] - c0[l] - c1[l]);
		Console.WriteLine(M);
	}
}