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: Time Limit Exceeded)

package main
import (
    "fmt"
    "math"
)

func main(){
    var N, K int
    var s string
    fmt.Scan(&N, &K, &s)
    fmt.Println(search(s, K, 0, 0, 0))
}

func search(s string, K, now, index int, co float64) float64{
    ans := 0.0
    for i:=index;i<len(s);i++{
        if s[i] == 48 {
            if K == now{
                return co
            }
            str, n := padding(s, i)
            co += float64(n - i + 1)
            
            ans = math.Max(search(str, K, now+1, n+1, co), ans)
            co, i = 0, n
        }else{
            co ++
        }
    }
    return math.Max(ans, co)
}

func padding(s string, index int) (string, int){
    str, n := []byte(s), 0
    for i := index; i < len(s) && s[i] == 48; i,n = i+1,n+1{
        str[i] = 49
    }
    return string(str), index+n-1
}