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 PyPy3 (2.4.0) (judge verdict: Wrong Answer)

N,K=map(int,input().split())
L=list(map(int,input()))
l=[]
countk=0
if L[0]==1:
    l.append(1)
else:
    l.append(-1)
    countk=1
for i in range(1,N):
    if L[i]==L[i-1]:
        if l[-1]<0:
            l[-1]+=-1
        else:
            l[-1]+=1
    else:
        if L[i]==1:
            l.append(1)
        else:
            l.append(-1)
            countk+=1
count=0
x=0
for i in range(len(l)):
    m=l[i]
    if l[i]<0:
        m=l[i]*(-1)
        count+=1
    x+=m
    if count==1:
        start=i-1
    if count==K:
        end=i
        if i==len(l)-1:
            break
        x+=l[i+1]
        break
X=x
if count<K:
    print(x)
else:
    for i in range(K,countk):
        if start==0:
            m=-1*l[start]
        else:
            m=-1*l[start]+l[start-1]
        if end+3==len(l):
            M=l[end+2]
        else:
            M=l[end+2]*(-1)+l[end+3]
        X=max(x,x+M-m)
        x=x+M-m
        start+=2
        end+=2
    print(X)