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 PyPy3 (7.3.0) (judge verdict: Wrong Answer)

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

S_zero={}
S_zero_group = 0
s_befor = ''
for s_idx,s in enumerate(S):
    if s != s_befor:
        if s == '0':
            S_zero_group += 1
            S_zero[S_zero_group] = [s_idx-1]
        elif s == '1':
            if S_zero_group in S_zero.keys():
                S_zero[S_zero_group].append(s_idx)
            
    s_befor = s
    
if S[-1] == '0':
    S_zero[S_zero_group].append(N)
    
if S_zero_group <= K:
    ans_ = N
else:   
    ans_=0
    for g_s in range(1,S_zero_group-K+2):
        g_e = g_s + K - 1
#         print('====',g_s,g_e)
        s = 0
        e = N-1

        if g_s != 1:
            s = S_zero[g_s-1][1]
        if g_e != S_zero_group:
            e = S_zero[g_e+1][0]

        ans= e-s+1
        print(e,s,ans)
        if ans > ans_:
            ans_=ans

print(ans_)