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: Wrong Answer)

function Main(input) {
  var list = input.split("\n");
  var nk = list[0].split(" ");
  var N = nk[0];
  var K = nk[1];
  var S = list[1].split("");
  S.map( function(value){
    return parseInt(value);
  })
  
  var count, rev;
  var state = 0;
  var maxcount = 0;
  var Sarray = new Array(0);
  
  count = 0
  state = 1;
  
  for(i=0;i<N;i++){
    if(S[i] != state) {
      state = 1 - state;
      Sarray.push(count);
      count = 1;
    } else count++;
  }
  Sarray.push(count);
  if(Sarray.length == 1) Sarray.push(0);
  if(Sarray.length % 2 == 0) Sarray.push(0);
  
  var ans = 0;
  for(i=0;i<Math.min(Sarray.length,2*K+1);i++){
    ans += Sarray[i];
  }
  
  var tmp;
  var Sn = Sarray.length;
  for(i=2*K+2;i<Sn;i+=2){
    tmp = ans - (Sarray[0] + Sarray[1]) + (Sarray[2*K+1] + Sarray[2*K]);
    Sarray.shift(2)
    if (tmp > ans) ans = tmp;
  }
  console.log(ans);
}
 
Main(require("fs").readFileSync("/dev/stdin", "utf8"));