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.util.*;
import static java.lang.Math.*;
import java.math.BigInteger;

public class Main {
    
	public static void main(String[] args){
		Scanner sc = new Scanner(System.in);
		
		// 入力
		int n = sc.nextInt();
		int k = sc.nextInt();
		String s = sc.next();
		
		// 計算
		int result = 0;
		char pre = '1';
		int cntOne = 0;
		int cntZero = 0;
		ArrayList<Integer> list = new ArrayList<Integer>();
		for(int i = 0; i < n; i++){
		    char c = s.charAt(i);
		    if(pre == '1' && c == '1'){
		        cntOne++;
		    }else if(pre == '1' && c == '0'){
		        list.add(cntOne);
		        cntZero = 1;
		        cntOne = 0;
		        pre = '0';
		    }else if(pre == '0' && c == '0'){
		        cntZero++;
		    }else if(pre == '0' && c == '1'){
		        list.add(cntZero);
		        cntOne = 1;
		        cntZero = 0;
		        pre = '1';
		    }
		}
		if(pre == '0'){
		    list.add(cntZero);
		    list.add(0);
		}else{
		    list.add(cntOne);
		}
		//System.out.println(list.toString());
		
		int loop = min(list.size(), 2*k + 1);
		int temp = 0;
		for(int i = 0; i < loop; i++){
		    temp += list.get(i);
		}
		result = temp;
		for(int i = loop; i < list.size(); i = i + 2){
		    temp += list.get(i);
		    temp += list.get(i + 1);
		    temp -= list.get(i - loop);
		    temp -= list.get(i + 1 - loop);
		    result = max(result, temp);
		}
		
		// 出力
		System.out.println(result);
        
	}
}