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()

zero_idx = []
list_ct = []
flg_1 = 0
flg_0 = 0
idx = 0
zero_ct = 0
zero = []
count = 0

if S[0] == '0':
    list_ct.append(0)

for i in S:
    if flg_1 == 0:
        if i == '1':
            if zero_ct:
                zero.append(zero_ct)
                zero_ct = 0
            flg_0 = 0
            count = 1
            flg_1 = 1
            idx += 1
        else:
            if flg_0 == 0:
                zero_ct += 1
                zero_idx.append(idx)
                flg_0 = 1
            else:
                zero_ct += 1
    else:
        if i == '1':
            count += 1
        else:
            flg_1 = 0
            flg_0 = 1
            list_ct.append(count)
            list_ct.append(0)
            if S[0] == '0':
                zero_idx.append(idx+1)
            else:
                zero_idx.append(idx)
            count = 0
            zero_ct = 1
            idx += 1

if count != 0:
    list_ct.append(count)
if S[-1] == '0':
    zero.append(zero_ct)

j = 0
for i in zero_idx:
    list_ct[i] = zero[j]
    j += 1

Max = 0
if zero_idx:
    if S[0] != '0':
        for i in range(len(zero_idx)-K+1):
            num = sum(list_ct[zero_idx[i]-1:zero_idx[i+K-1]+2])
            if num > Max:
                Max = num
    else:
        for i in range(len(zero_idx)-K+1):
            if i != 0:
                num = sum(list_ct[zero_idx[i]-1:zero_idx[i+K-1]+2])
                if num > Max:
                    Max = num
            else:
                num = sum(list_ct[zero_idx[i]:zero_idx[i+K-1]+2])
                if num > Max:
                    Max = num
else:
    Max = sum(list_ct)

print(Max)