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 Go (1.6) (judge verdict: Accepted)

package main

import (
	"bufio"
	"fmt"
	"os"
	"strconv"
)

var (
	BufferSize = 10 * 10 * 10 * 10 * 10 * 10
)

func scanInt(sc *bufio.Scanner) int {
	if !sc.Scan() {
		panic(nil)
	}

	i, err := strconv.Atoi(sc.Text())
	if err != nil {
		panic(err)
	}

	return i
}

func scanStr(sc *bufio.Scanner) string {
	if !sc.Scan() {
		panic(nil)
	}

	return sc.Text()
}

func getRev(before byte) byte {
	if before == '0' {
		return '1'
	}
	return '0'
}

func cSum() {
	sc := bufio.NewScanner(os.Stdin)
	buf := make([]byte, BufferSize)
	sc.Buffer(buf, BufferSize)
	sc.Split(bufio.ScanWords)

	n := scanInt(sc)
	k := scanInt(sc)
	s := scanStr(sc)

	// fmt.Printf("n = %+v\n", n)
	// fmt.Printf("k = %+v\n", k)
	// fmt.Printf("s = %+v\n", s)

	csum := make([]int, 0, len(s)+10)

	before := s[0]
	csum = append(csum, 1)
	for i := 1; i < n; i++ {
		if s[i] != before {
			csum = append(csum, csum[len(csum)-1]+1)
		} else {
			csum[len(csum)-1]++
		}
		before = s[i]
	}

	// fmt.Printf("csum = %+v\n", csum)

	max := 0
	rightIndexFunc := zeroRightIndex
	if s[0] != '0' {
		rightIndexFunc = oneRightIndex
	}
	leftIndexFunc := zeroLeftIndex
	if s[0] != '0' {
		leftIndexFunc = oneLeftIndex
	}
	for i := 0; i < len(csum); i += 2 {
		rightIndex := rightIndexFunc(i, k)
		var right int
		if rightIndex > len(csum)-1 {
			rightIndex = len(csum) - 1
		}
		right = csum[rightIndex]

		leftIndex := leftIndexFunc(i)
		var left int
		if leftIndex < 0 {
			leftIndex = -1
			left = 0
		} else {
			left = csum[leftIndex]
		}
		length := right - left
		// fmt.Printf("[%d](%d) - [%d](%d): %d\n", leftIndex, left, rightIndex, right, length)
		if length > max {
			max = length
		}
	}

	fmt.Printf("%d\n", max)
}

func zeroLeftIndex(i int) int {
	return i - 2
}

func oneLeftIndex(i int) int {
	return i - 1
}

func zeroRightIndex(i int, k int) int {
	return i + 2*k - 1
}

func oneRightIndex(i int, k int) int {
	return i + 2*k
}

func scaleUp() {
	sc := bufio.NewScanner(os.Stdin)
	buf := make([]byte, BufferSize)
	sc.Buffer(buf, BufferSize)
	sc.Split(bufio.ScanWords)

	n := scanInt(sc)
	k := scanInt(sc)
	s := scanStr(sc)

	// fmt.Printf("n = %+v\n", n)
	// fmt.Printf("k = %+v\n", k)
	// fmt.Printf("s = %+v\n", s)

	flipCount := 0
	prev := s[0]
	max := 0
	length := 0
	left := 0
	right := 1

	// left move loop
	for left < n {
		// right move lop
		for right < n {
			// count 0 -> 1 or 1 -> 0
			if s[right] != prev {
				flipCount++
			}

			// memory prev
			prev = s[right]

			if s[left] == '0' {
				// right limit if 0 start
				if flipCount > 2*k-1 {
					break
				}
			} else {
				// right limit if 1 start
				if flipCount > 2*k {
					break
				}
			}
			right++
			// fmt.Printf("right++: left = %+v, right = %+v, length = %+v\n", left, right, right-left)
		}

		// update max
		length = right - left
		if length > max {
			max = length
			// fmt.Printf("  max changed: left = %+v, right = %+v, length = %+v\n", left, right, right-left)
		}
		// fmt.Printf("  left = %+v, right = %+v, length = %+v, flipCount = %+v\n", left, right, right-left, flipCount)

		// no more max length
		if right >= n {
			break
		}

		index := left
		left++
		// left move
		for left < right {
			if s[left] != s[index] {
				flipCount--
				break
			}
			left++
		}
		// fmt.Printf("  left++: left = %+v, right = %+v, length = %+v, flipCount = %+v\n", left, right, right-left, flipCount)
	}

	fmt.Printf("%d\n", max)
}

func main() {
	// cSum()
	scaleUp()
}