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 Python (3.4.3) (judge verdict: Wrong Answer)

n,k=map(int,input().split())
s=input()

num_cnt=[]
if s[0]=='1':
  num_cnt.append(0)

cnt=1
for i in range(1,n):
  if s[i]==s[i-1]:
    cnt+=1
  else:
    num_cnt.append(cnt)
    cnt=1
num_cnt.append(cnt)

leng=len(num_cnt)
if leng//2>k:
  ans=sum(num_cnt[:2*k])
  tot=ans
  
  if leng%2==0:
    limit=leng//2-k
  else:
    num_cnt.append(0)
    limit=leng//2-k+1
  
  #print(ans)
  #print(num_cnt)
  tmp=num_cnt[2*k]+num_cnt[2*k+1]-num_cnt[0]
  #print(tmp)
  tot+=tmp
  if tot>ans:
    ans=tot
  
  for i in range(1,limit):
    tmp=num_cnt[2*(i+k)]+num_cnt[2*(i+k)+1]-num_cnt[2*i]-num_cnt[2*i+1]
    #print(tmp)
    tot+=tmp
    if tot>ans:
      ans=tot
else:
  ans=n
print(ans)