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.Text;
using System.Collections.Generic;
using System.Linq;
using E = System.Linq.Enumerable;
 
class Program
 {

      
        static void Main(string[] args)
        {
          //入力を受け取る
          var NK = Console.ReadLine().Split(' ').Select(x => double.Parse(x)).ToArray();
          var N = NK[0];
          var K = NK[1];
          var S = Console.ReadLine();
          
          var tyoku = new List<int>();
          var saka  = new List<int>();
          var all   = new List<int>();
          for(int i = 0 ; i < N ; i++){
            var sentou = S[i];
            var count = 1;
            i++;
            while(i < N && sentou == S[i]){
              i++;
              count++;
            }
            if(sentou == '1'){
              saka.Add(count);
              all.Add(count);
            }else{
              tyoku.Add(count);
              all.Add(count);
            }
            i--;
          }
          var tyo = tyoku.ToArray();
          var sa =  saka.ToArray();
          var AllA =  all.ToArray();
          
          var sum = new int[AllA.Length+1];
          sum[0] = 0;
          for(int i = 1 ; i < AllA.Length+1 ; i++){
            sum[i] = sum[i-1]+AllA[i-1];
          }
          
          var res = 0;
          if(S[0] == '1'){
            for(int i = 1;i < sum.Length;i += 2){
              var start = i;
              var end = (int) Math.Min(i+2*K,sum.Length-1);
              var cum = sum[end]-sum[start-1];
              if(res < cum){
                res = cum;
              }
            }
          }else{
             var start = 1;
             var end = (int) Math.Min(2*K,sum.Length-1);
             res = sum[end]-sum[start-1];
             for(int i = 2;i < sum.Length;i += 2){
               start = i;
               end = (int) Math.Min(i+2*K,sum.Length-1);
               var cum = sum[end]-sum[start-1];
               if(res < cum){
                 res = cum;
               }
             }
          }
          Console.WriteLine(res);
        }
}