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: Runtime Error)

#define _USE_MATH_DEFINES
#include <iostream>
#include <cstdio>
#include <cstdlib>
#include <algorithm>
#include <vector>
#include <cstring>
#include <queue>
#include <functional>
#include <set>
#include <map>
#include <string>
#include <cmath>
#include <math.h>
#include <complex>
#include <cassert>
#define rep(i,a,b) for (int i = (a); i < (b); i++)
#define case(i) cout<<"Case #"<<i<<": "
using namespace std;
typedef long long int ll;
typedef pair<ll, ll> pr;
typedef complex<double> com;
const int mod = 1e9 + 7;
const int MOD = 998244353;
const ll INF = 1e18;


int main() {
	int n, k; cin >> n >> k;
	string s; cin >> s;
	vector<int> a;
	int cnt = 1;
	rep(i, 1, n) {
		if (s[i] == s[i - 1]) cnt++;
		else {
			a.push_back(cnt);
			cnt = 1;
		}
	}
	a.push_back(cnt);
	int maxx=0;
	rep(i, 0, min((int) a.size(), 2*k)) {
		maxx += a[i];
	}
	if (s[0] == '1' && a.size() > 2 * k) maxx += a[2 * k];
	rep(i, 0, a.size() - k) {
		if (a[i + k] - a[i] > 0) maxx += a[i + k] - a[i];
		i++;
	}
	cout << maxx << endl;
	return 0;
}