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 (3.8.2) (judge verdict: Wrong Answer)

N, K=map(int,input().split())
S = str(input())

print(N)
print(K)

# make seq_cnt_list
seq_cnt_list = []
seq_cnt = 0
last_man = ""
for i in range(N):
    cur_man = S[i]
    if cur_man != last_man:
        #print("S[%d]=%s is change" % (i, S[i]))
        if seq_cnt > 0:
            if last_man == "0":
                seq_cnt *= -1
            seq_cnt_list.append(seq_cnt)
        seq_cnt = 1
    else:
        #print("S[%d]=%s is same" % (i, S[i]))
        seq_cnt += 1
    last_man = cur_man
if seq_cnt > 0:
    if last_man == "0":
        seq_cnt *= -1
    seq_cnt_list.append(seq_cnt)

print(seq_cnt_list)

for k in range(K):
    seq_cnt_list_size = len(seq_cnt_list)
    if (seq_cnt_list_size < 2) or (seq_cnt_list_size == 3 and seq_cnt_list[0] > 0):
        seq_cnt_list = [sum(map(abs, seq_cnt_list))]
        break
    else:
        max_pos = 0
        max_val = 0
        for i in range(seq_cnt_list_size):
            if seq_cnt_list[i] < 0:
                val = seq_cnt_list[i] * -1
                if i > 0:
                    val += seq_cnt_list[i - 1]
                if i < seq_cnt_list_size - 1:
                    val += seq_cnt_list[i + 1]
                if val > max_val:
                    max_val = val
                    max_pos = i
        start_pos = max_pos - 1 if max_pos > 0 else max_pos
        end_pos = max_pos + 1 if max_pos < seq_cnt_list_size - 1 else max_pos
        seq_cnt_list[start_pos: end_pos + 1] = [max_val]

print(max(seq_cnt_list))