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())
s=input()
d=[]
f=True

if s[0]=="0":
    d.append(0)
    f=False

seq=1
for i in range(1,n):
    if s[i]=="0" and not f:
        seq+=1
    elif s[i]=="0" and f:
        f=False
        d.append(seq)
        seq=1
    elif s[i]=="1" and f:
        seq+=1
    else:
        f=True
        d.append(seq)
        seq=1
    if i==n-1:
      d.append(seq)
if s[-1]=="0":
    d.append(0)
l=len(d)
res=[0]*(l+1)
res[0]=0
for i in range(1,l+1):
    res[i]=res[i-1]+d[i-1]
ans=1
for i in range(1,n):
    if i%2==1:
        continue
    if 2*k+i-1>l:
      break
    a=res[2*k+i-1]-res[i-2]
    if a>ans:
        ans=a
print(ans)