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: Runtime Error)

package main

import (
	"fmt"
)

func main() {
	var n, k int
	fmt.Scanf("%d %d", &n, &k)

	var input string
	fmt.Scan(&input)
	inputRune := []rune(input)

	fb := inputRune[0] == []rune("0")[0]
	lines := make([]int, 0)
	for i := 0; i < n; i++ {
		if len(lines) == 0 || inputRune[i-1] != inputRune[i] {
			lines = append(lines, 0)
		}
		lines[len(lines)-1] += 1
	}

	var output int
	lineLength := len(lines)

	var preValue int
	if fb {
		// indexが0の時を求める
		var result int
		for i := 0; i < 2*k; i++ {
			if i > lineLength {
				break
			}

			result += lines[i]
		}

		output = result
		preValue = result

		// indexが0以上の時を求める
		for i := 1; i*2-1 < lineLength; i++ {
			result := preValue

			// 前のやつを引く
			for j := 2*(i-1) - 1; j < 2*i-1; j++ {
				if j < 0 {
					continue
				}
				result -= lines[j]
			}

			// 次のやつを足す
			for j := 2 * (i - 1 + k); j <= 2*(i+k); j++ {
				if j >= len(lines) {
					break
				}
				result += lines[j]
			}

			if result > output {
				output = result
			}
			preValue = result
		}
	} else {
		// indexが0の時を求める
		var result int
		for j := 0; j <= k*2; j++ {
			if j >= lineLength {
				break
			}

			result += lines[j]
		}

		output = result
		preValue = result

		// indexが0以上の時を求める
		for i := 1; i*2 < lineLength; i++ {
			result := preValue

			// 前のやつを引く
			for j := 2 * (i - 1); j < 2*i; j++ {
				result -= lines[j]
			}

			// 次のやつを引く
			for j := 2*(i+k-1) + 1; j <= 2*(i+k); j++ {
				if j >= lineLength {
					break
				}

				result += lines[j]
			}

			if result > output {
				output = result
			}
			preValue = result
		}
	}
	fmt.Println(output)
}