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 Kotlin (1.0.0) (judge verdict: Runtime Error)

import java.util.*

fun main(args: Array<String>) {
	val scanner = Scanner(System.`in`)
	val N = scanner.nextInt()
	val K = scanner.nextInt()
	val S = scanner.next()
	scanner.close()
	val array = ArrayList<TwoNum>()
	var first = -1
	for (i in 0 until N) {
		if (S[i] == '1') {
			if (first == -1) first = i
		} else {
			if (first != -1) {
				array.add(TwoNum(first, i - 1))
				first = -1
			}
		}
	}
	if (first != -1) array.add(TwoNum(first, N - 1))
	if (array[0].first != 0) {
		array.reverse()
		array.add(TwoNum(0, 0))
		array.reverse()
	}
	if (array[array.size - 1].last != N - 1) {
		array.add(TwoNum(N - 1, N - 1))
	}
	if (array.size - 1 <= K) {
		print(N)
		return
	}
	var max = 0
	for (i in 0 until array.size - K) {
		val temp = array[i + K].last - array[i].first + 1
		max = if (temp > max) temp else max
	}
	print(max)
}

class TwoNum (val first: Int, val last: Int)