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 = list(input())
#print(S)
ss = [] # set of 01 sequense
s = []
s_prev = S[0]
for i in range(N):
    si = int(S[i])
    #print(s_prev, si)
    if int(si) != int(s_prev):
        #print("push")
        ss.append(s)
        s = [si]
    else:
        s.append(si)
    s_prev = si
ss.append(s)
#print(ss)
result = 1
# get max len of ss[i]
for k in range(K):
    max_ss = 0
    max_i = -1
    for i in range(len(ss)):
        if ss[i][0] == 1: continue
        if i > 0:
            if i < len(ss) - 1:
                len_ss = len(ss[i-1]) + len(ss[i]) + len(ss[i+1])
            else:
                len_ss = len(ss[i-1]) + len(ss[i])
        else:
            if i < len(ss) - 1:
                len_ss = len(ss[i]) + len(ss[i+1])
            else:
                len_ss = len(ss[i])

        #print("i", i, len_ss)
        if len_ss > max_ss:
            max_i = i
            max_ss = len_ss
    #print(max_i, max_ss)
    if max_i != -1:
        # reverse ss
        if max_i > 0:
            if max_i < len(ss) - 1:
                ss[max_i - 1] = ss[max_i - 1] + [1 for _ in range(len(ss[max_i]))] + ss[max_i + 1]
                del ss[max_i + 1]
                del ss[max_i]
            else:
                ss[max_i - 1] = ss[max_i - 1] + [1 for _ in range(len(ss[max_i]))]
                del ss[max_i]
        else:
            if max_i < len(ss) - 1:
                ss[max_i - 1] = [1 for _ in range(len(ss[max_i]))] + ss[max_i + 1]
                del ss[max_i]
            else:
                ss[max_i - 1] = ss[max_i - 1]
        #print("ss", ss)
        result = max_ss
print(result)