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 = [int(x) for x in input().split()]

S = input()
a= S[0]
b = int(S[0])
table = []
c = 0
for s in S:
    if int(s) == b:
        c += 1
    else:
        b = not(b)
        table.append(c)
        c = 1

table.append(c)

if a =='0':
    N = 2*K+1
    ans = sum(table[0:2*K])
    for i in range(1,len(table),2):
        if sum(table[i:i+N])>ans:
            ans = (table[i:i+N])
            #ans = max(ans,sum(table[i:i+1+2*K]))

else:
    ans =0
    N = 2*K +1
    for i in range(0,len(table),2):
        if sum(table[i:i+N])>ans:
            ans = sum(table[i:i+N])
        #ans = max(ans,sum(table[i:i+2*K+1]))
#print(table)
print(ans)