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;

namespace D___Handstand
{
    class Program
    {
        static void Main(string[] args)
        {
            var read = Console.ReadLine().Split(' ');
            var N = int.Parse(read[0]);
            var K = int.Parse(read[1]);

            var S = Console.ReadLine();

            var switch01 = new List<int>();
            switch01.Add(0);

            for(int i = 1 ; i < S.Length ; i++) if(S[i] != S[i-1]) switch01.Add(i);
            switch01.Add(S.Length);

            var continuousHandstand = new List<int>();
            
            for(int i = 0 ; i < switch01.Count-1 ; i++) continuousHandstand.Add(S[switch01[i]] == '0' ? switch01[Math.Min(switch01.Count-1,i+2*K)]-switch01[i] : switch01[Math.Min(switch01.Count-1,i+2*K+1)]-switch01[i]);
            
            Console.WriteLine(continuousHandstand.Max());
        }
    }
}