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 Julia (0.5.0) (judge verdict: Accepted)

parseInt(x) = parse(Int, x)
parseBigInt(x) = parse(BigInt, x)
parseFloat(x) = parse(Float64, x)
parseBigFloat(x) = parse(BigFloat, x)
parseMap(x::Array{SubString{String},1}) = map(parseInt, x)

function main()
    n,k=parseMap(split(readline()))
    s=chomp(readline())
    cnt=Vector{Int}()
    res=1
    for i in 2:n+1
        if i==n+1 || s[i]!=s[i-1]
            push!(cnt,res*ifelse(s[i-1]=='0',-1,1))
            res=1
        else
            res+=1
        end
    end
    l=length(cnt)
    ans=0
    ruiseki=[0 for i in 1:l+1]
    for i in 1:l
        ruiseki[i+1]=ruiseki[i]+abs(cnt[i])
    end
    for i in 1:l
        if cnt[i]>0
            m=min(i+2k,l)
        else
            m=min(i+2k-1,l)
        end
        ans=max(ans,ruiseki[m+1]-ruiseki[i])
    end
    println(ans)
end
main()