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
#include<cstdio>

char s[200000];
int t[500000];

int main(void) {
    int n,k;
    scanf("%d%d",&n,&k);
    k = 2*k+1;
    scanf("%s",s);

    char last = '0';
    int j=2;
    for(int i=0; i<n; i++) {
        if(s[i] == last) {
            t[j]++;
        } else {
            t[++j] = 1;
            last = s[i];
        }
    }
    ++j;
    j+=2*k+10;

    for(int i=0; i<j; i++) {
        /* printf("%d ", t[i]); */
        t[i+1] += t[i];
    }
        /* printf("\n"); */

    int m = 0;
    for(int i=0; i+k<j; i+=2) {
        if(m < t[i+k]-t[i]) m = t[i+k]-t[i];
    }
    printf("%d\n", m);
}
