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 Python (3.4.3) (judge verdict: Runtime Error)

package main

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

var sc = bufio.NewScanner(os.Stdin)

func ini() {
	var buf = make([]byte, 10000)
	sc.Buffer(buf, 1000000)
}

func nextLine() string {
	sc.Scan()
	return sc.Text()
}

func max(a, b int) int {
	if a > b {
		return a
	}
	return b
}

func main() {
	ini()
	line1 := nextLine()
	NK := strings.Split(line1, " ")
	N, _ := strconv.Atoi(NK[0])
	K, _ := strconv.Atoi(NK[1])
	S := nextLine()
	l := make([]int, 0)
	if string(S[0]) == "0" {
		l = append(l, 0)
	}
	for i := 0; i < N; {
		j := i
		for j < N && S[j] == S[i] {
			j++
		}
		l = append(l, j-i)
		i = j
	}
	if string(S[N-1]) == "0" {
		l = append(l, 0)
	}

	sums := make([]int, len(l)+1)
	for i := 0; i < len(l); i++ {
		sums[i+1] = sums[i] + l[i]
	}
	ans := 0
	for left := 0; left < len(sums); left += 2 {
		right := left + 2*K + 1
		if right >= len(sums) {
			right = len(sums) - 1
		}
		ans = max(ans, sums[right]-sums[left])
	}
	fmt.Println(ans)
}