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 C++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include <bits/stdc++.h>
using namespace std;

int main(){
	int n, k;
	string st;
	cin >> n >> k;
	cin >> st;
	if(n==0){
		cout << 0 << endl;
		return 0;
	}
	vector<int> vec;
	vector<int> vec2;	
	if(n<=2){
		char last=st[0];
		for(int i=0; i<st.size(); i++){
			if(st[i]!=last && k>0){
				cout << n << endl;
				return 0;
			}
		}
		cout << last << endl;
		return 0;
	}
	int result=0;
	for(int i=0; i<n; i++){
		if(st[i]=='0'){
			vec.push_back(result);
			result=0;
			int num=1;
			i++;
			while(st[i]=='0'){
				i++;
				num++;
			}
			result++;
			vec.push_back(num);
		}
		else if(i==n-1){
			vec.push_back(result+1);
		}
		else{
			result++;
		}
	}
	int fin=0;
	for(int j=0; j<k; j++){
		int max=0;
		int l=0, t=2;
		n=vec.size();
		for(int i=1; i<n; i++){
			if(i==n-1){
				int nu=vec[i-1]+vec[i];
				if(nu>max){
					max=nu;
					l=i-1;
					t=i;
				}
			}
			else{
				int nu=vec[i-1]+vec[i]+vec[i+1];
				if(nu>max){
					max=nu;
					l=i-1;
					t=i+1;
					i++;
				}
			}
		}
		fin=max;
		if(l%2==0){
			if(l-1>=0 && t+1<n){
				for(int k=l; k<=t; k++)
					vec[k]=max;
				vec.erase(vec.begin()+l, vec.begin()+t);
			}
			else if(l-1>=0 && t+1>=n){
				vec[t]=0;
				for(int k=l; k<t; k++)
					vec[k]=max;
				vec.erase(vec.begin()+l, vec.begin()+t-1);

			}
			else{
				vec[l]=0;
				for(int k=l+1; k<=t; k++)
					vec[k]=max;
				vec.erase(vec.begin()+l+1, vec.begin()+t-1);

			}
		}
		else{
			for(int k=l; k<=t; k++)
				vec[k]=max;
			vec.erase(vec.begin()+l, vec.begin()+t);

		}
	}
	cout << fin << endl;
}