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: Time Limit Exceeded)

import sys
sys.setrecursionlimit(10 ** 9)
N,K=map(int,input().split())
S=input()

#N=14
#K=2
#S="11101010110011"

LIST=[[[0] for j in range (2)]for i in range(N)]

t=S[0]
c=0
k=0
for i in range(N):
    if(t!=S[i]):
        LIST[k][0]=c
        LIST[k][1]=t
        t=S[i]
        k+=1
        c=0
    c+=1

LIST[k][0]=c
LIST[k][1]=t
LIST=LIST[0:k+1]
MAX=0

def calc(i,s,K):
    global MAX
    MAX=max(MAX,s)
    if(i==len(LIST)):
        return

    if(LIST[i][1]=="1"):
        s+=LIST[i][0]
        MAX=max(MAX,s)
        i+=1
        if(i==len(LIST)):
            return
    
    if(K>=1):
        calc(i+1,s+LIST[i][0],K-1)
    calc(i+1,0,K)

calc(0,0,K)
print(MAX)