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: Wrong Answer)

package main

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

var sc *bufio.Scanner

func nextInt() int {
	sc.Scan()
	i, e := strconv.Atoi(sc.Text())
	if e != nil {
		panic(e)
	}
	return i
}

func answer(reader io.Reader, writer io.Writer) {
	sc = bufio.NewScanner(reader)
	sc.Split(bufio.ScanWords)
	n := nextInt()
	k := nextInt()
	sc.Scan()
	in := sc.Text()
	a := make([]int, n+2)
	a[0] = 0
	last := "1"
	ind := 0
	//fmt.Printf("%d, %d, %s\n", n, k, in)
	for i := 0; i < len(in); i++ {
		c := string(in[i])
		if (c != "0" && c != "1") || ind == n || i >= n {
			break
		}
		if last != c {
			ind++
			last = c
		}
		a[ind]++
	}
	//fmt.Printf("%v\n", a)
	sum := 0
	max := 0
	for i := 0; i < n+2; i++ {
		sum += a[i]
		if i > k*2 {
			sum -= a[i-k*2-1]
		}
		if i%2 == 0 && max < sum {
			max = sum
		}
		//fmt.Printf("i: %v, sum: %v, max: %v\n", i, sum, max)
	}
	_, _ = fmt.Fprintf(writer, "%d\n", max)
}

func main() {
	answer(os.Stdin, os.Stdout)
}