/*
    cogs 942. [東方S3] 比那名居天子
    
    二分水题
     
    二分所求区间长度
    判断后缩小范围即可 
*/
#include <cstring>
#include <cstdio>

#define Max 1000000

void read (int &now)
{
    now = 0;
    register char word = getchar ();
    while (word < ‘0‘ || word > ‘9‘)
        word = getchar ();
    while (word >= ‘0‘ && word <= ‘9‘)
    {
        now = now * 10 + word - ‘0‘;
        word = getchar ();
    }
}

char line[Max];

int N, K;

bool Judge (int key)
{
    int Count = 0;
    for (register int i = 0; i < N; i ++)
        if (line[i] == ‘1‘)
        {
            i += key - 1;
            Count ++;
            if (Count > K)
                return false;
        }
    return true;
}

int main (int argc, char *argv[])
{
    freopen ("tenshi.in", "r", stdin);
    freopen ("tenshi.out", "w", stdout);
    
    read (N);
    read (K);
    
    scanf ("%s", line);
    
    int pos = 0;
    for (pos = 0; line[pos] == ‘0‘; pos ++);
    if (pos == N)
    {
        putchar (‘0‘);
        return 0;
    }
    
    register int Answer;
    for (register int l = 1, r = (N << 1), Mid; l <= r; )
    {
        Mid = l + r >> 1;
        if (Judge (Mid))
        {
            r = Mid - 1;
            Answer = Mid;
        }
        else 
            l = Mid + 1;
    }
    
    printf ("%d", Answer);
    return 0;
}