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.

Examples

Input

5 1
00010


Output

4


Input

14 2
11101010110011


Output

8


Input

1 1
1


Output

1
import java.io.*;
import java.util.*;
import java.util.function.*;
import java.util.regex.*;
import java.util.stream.*;

final class Solver {
	void solve(Supplier<String> sc) {
		int N = Integer.parseInt(sc.get());
		int K = Integer.parseInt(sc.get());
		String S = sc.get();
		Pattern pattern = Pattern.compile("1+");
		Matcher matcher = pattern.matcher(S);
		int[] starts, ends;
		{
			IntStream.Builder startsBuilder = IntStream.builder();
			IntStream.Builder endsBuilder = IntStream.builder();
			while (matcher.find()){
				startsBuilder.add(matcher.start());
				endsBuilder.add(matcher.end());
			}
			starts = startsBuilder.build().toArray();
			ends = endsBuilder.build().toArray();
		}

		if (starts.length == 0){
			System.out.println(N);
			return;
		}

		int zeros = starts.length - 1;
		if (starts[0] != 0) zeros += 1;
		if (ends[ends.length - 1] != N) zeros += 1;

		if (K >= zeros) {
			System.out.println(N);
			return;
		}


		int max = 0;
		for (int i = 0; i < ends.length; i++) {
			max = Math.max(max, ends[i] - starts[Math.max(i - K, 0)]);
		}
		if (starts[0] != 0){
			max = Math.max(max, ends[Math.min(K, ends.length) - 1]);
		}
		if (ends[ends.length - 1] != N){
			max = Math.max(max, N - starts[Math.max(starts.length - K, 0)]);
		}

		System.out.println(max);
	}
}

class Main {
	public static void main(String... args) {
		new Thread(null, () -> {
			BufferedReader reader = new BufferedReader(new InputStreamReader(System.in));
			new Solver().solve(new Supplier<String>() {
				StringTokenizer line;

				public String get() {
					while (line == null || !line.hasMoreTokens()) try {
						line = new StringTokenizer(reader.readLine());
					} catch (IOException e) {
						throw new UncheckedIOException(e);
					}
					return line.nextToken();
				}
			});
			System.out.flush();
		}, "", Runtime.getRuntime().maxMemory()).start();
	}
}