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 setUp(input) {
  input = input.split("\n");
  N = Number(input[0].split(' ')[0]);
  K = Number(input[0].split(' ')[1]);
  S = input[1];
  main();
}
function main() {
  oddList = [];
  evenList = [];
  S.split('0').forEach(function (d, i) {
    if (d.length) {
      oddList.push(d.length);
    }
  });
  S.split('1').forEach(function (d, i) {
    if (d.length) {
      evenList.push(d.length);
    }
  });

  var maxLen = Math.min(oddList.length, evenList.length);
  ruiseki = [0];
  var sum = 0;
  for (var i = 0; i < maxLen; i++) {
    sum += oddList[i] + evenList[i];
    ruiseki.push(sum);
  }
  if (oddList.length > evenList.length) {
    ruiseki[maxLen] += oddList[maxLen];
  } else if (oddList.length < evenList.length) {
    ruiseki.push(sum + evenList[maxLen]);
  }

  var maxLen = ruiseki.length - K;
  var count = 0;
  for (var i = 0; i <= maxLen; i++) {
    var target = ruiseki[i + K] - ruiseki[i];
    if (target > count) {
      count = target;
    }
  }
  console.log(count);
}

setUp(require("fs").readFileSync("/dev/stdin", "utf8"));
// setUp('14 2\n11101010110011')
// setUp('14 2\n00010101001100')