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.*;
public class Main {
	public static void main(String[] args){
		Scanner sc = new Scanner(System.in);
		int num = sc.nextInt();
		int k = sc.nextInt();
		String s = sc.next();
        String[] line = new String[num];
        line = s.split("");
        String former = line[0];
        int check = 0;
        int count = 1;
        int count2 = 0;
        int index = 0;
        int sum = 0;
        int max = 0;
        int temp = 0;
        List<Integer> counter = new ArrayList<Integer>();
        List<Integer> counter2 = new ArrayList<Integer>();
        if(line[0].equals("0")) check = 1;
        if(line.length == 1) {
            counter.add(count);
            counter2.add(count);
        }
        for(int i=1; i<num; i++){
          if(line[i].equals(former)){
            count++;
          }
          else{
            check++;
            count++;
            if(line[i].equals("0")) former = "0";
            else former = "1";
          }
          if(check == 2) count2++;
          if(check == 3){
            counter.add(count-1);
            counter2.add(count-1-temp);
            count = count2+1;
            temp = count2;
            count2 = 0;
            check = 1;
          }
          if(i+1 >= num) {
            counter.add(count);
            counter2.add(count-temp);
            break;
          }
        }
        temp = 0;
        while(true){
          temp = index;
          sum += counter.get(index);
          index++;
          for(int j=1; j<k; j++){
             if(index >= counter2.size()) break;
             sum += counter2.get(index);
             index++;
          }
          if(max < sum) max = sum;
          sum = 0;
          index = temp + 1;
          if(index+k > counter2.size()) break;
        }
        System.out.println(max);
	}
}
