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=list(input())
st=[]
en=[]
if s[0]=="1":
    st.append(0)
for i in range(1,n):
    if s[i-1]=="0" and s[i]=="1":
        st.append(i)
    if s[i-1]=="1" and s[i]=="0":
        en.append(i)
if s[n-1]=="1":
    en.append(n-1)
ans=0
if len(en)+1<=k:
    print(n)
    exit()
if len(en)<=k and s[0]=="1":
    print(n)
    exit()
if len(en)<=k and s[n-1]=="1":
    print(n)
    exit()
if len(en)-1<=k and s[n-1]=="1" and s[0]=="1":
    print(n)
    exit()
    
if len(en)<=k:
    k=len(en)
for i in range(len(en)-k):
    ans=max(ans,en[i+k]-st[i]+1)
if s[0]=="0":
    ans=max(ans,en[k-1])
if s[n-1]=="0":
    ans=max(ans,n-st[len(st)-k]+1)
print(ans)