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 JavaScript (node.js v5.12) (judge verdict: Time Limit Exceeded)

const main = (input) => {
  var ip = input.trim().split("\n")[0].split(" ");
  var N = ip[0]-0;
  var K = ip[1]-0;
  if(N<=K/2){
    console.log(N);
    return;
  }
  var inputs = input.trim().split("\n")[1].split("");
  var ans = 0;
  var map = {};
  for(var s=0;s<inputs.length;s++){
    var cnt = 0, zflg=false,zcnt=0, tans = 0;
    var zst=-1;
    if(s == 0 || (inputs[s-1] == 0 && inputs[s] == 1)){
      for(var e=s;e<inputs.length;e++){
        if(inputs[e]==0 && zflg==false){
          if(map[zst]){
            e+=map[zst];
            tans+=map[zst];
            zflg = true;
            continue;
          }
          zst=e;
          zflg = true;
          zcnt++;
          if(K<zcnt) break;
        }else if(inputs[e] == 1){
          if(zflg){
            map[zst] = e-zst;
            zflg = false;
            zst = -1;
          }
        }
        tans++;
      }
      ans = Math.max(ans, tans);
      if(ans >= inputs.length-s) break;
    }
  }
  console.log(ans);
}

main(require('fs').readFileSync('/dev/stdin', 'UTF-8'));