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: Runtime Error)

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

l=[]
state=0
one=0
zero=0
for i in range(len(s)):
    if s[i]=='0':
        if i+1 == len(s) or s[i+1]=='1':
            l.append(one)
            l.append(zero+1)
            one=0
            zero=0
        else:
            zero+=1
    elif s[i]=='1':
        one+=1
if one!=0:
    l.append(one)

if s[0]=='0':
    l = [0]+l
if s[-1]=='1':
    l.append(0)



max_0=-1
for i in range(len(l)):
    if i%2 == 0:
        continue
    if l[i] > max_0:
        max_0 = l[i]

index = 0
for i in range(len(l)):
    if l[i]==max_0:
        index = 0
        break

ans=0
ans+=l[index]
l[index-1]=l[index]+l[index+1]
del l[index]
del l[index]
for _ in range(k):
    if len(l)<3:
        break
    if l[index-2]+l[index-1]+l[index] > l[index]+l[index+1]+l[index+2]:
        ans+=l[index-2]+l[index-1]
        del l[index-2]
        del l[index-1]
    else:
        ans+=l[index+1]+l[index+2]
        del l[index+1]
        del l[index+2]

print(ans)