DHBB112021_BITSTR

#define task "BITSTR"

#include <iostream>
#include <cstdio>
#include <set>
#include <algorithm>

using namespace std;

using ll = long long;
using ld = long double;

void read(int &x)
{
    x = 0;
    register int c;
    while ((c = getchar()) && (c > '9' || c < '0'))
        ;
    for (; c >= '0' && c <= '9'; c = getchar())
        x = x * 10 + c - '0';
}

void readstr(string &s)
{
    s.clear();
    register int c;
    while ((c = getchar()) && (c > '1' || c < '0'))
        ;
    for (; c >= '0' && c <= '1'; c = getchar())
        s.push_back(c);
}

constexpr int N = 2e5 + 5;
constexpr int Inf = 1e9 + 7;
int n, k, l[N], r[N], a[N], v[N], m(0);
string s;

#define bit(i, x) (((x) >> (i)) & 1)

void Read()
{
    cin >> n >> k >> s;
    s = " " + s;
}

void Sub_3()
{
    for (int i = 1, j = 1; i <= n; ++i)
    {
        while (j <= n && s[i] == s[j])
            ++j;
        a[++m] = j - i;
        l[m] = r[m] = m;
        i = j - 1;
    }

    if (m <= k)
    {
        cout << 0;
        return;
    }

    if (k == 1)
    {
        cout << min(count(s.begin(), s.end(), '0'), count(s.begin(), s.end(), '1'));
        return;
    }

    int ans(Inf);

    for (int i = 0; i < 2; ++i)
        for (int j = 0; j < 2; ++j)
        {
            int res(0);
            if (i)
                res += a[1];
            if (j)
                res += a[m];

            struct com
            {
                bool operator()(const int &x, const int &y) const
                {
                    return v[x] < v[y] || (v[x] == v[y] && x < y);
                }
            };

            set<int, com> q;

            for (int t = 2 + i; t <= m - 1 - j; ++t)
            {
                r[t] = t;
                l[t] = t;
                v[t] = a[t];
                q.insert(t);
            }

            int sz(q.size() + 2);

            while (sz > k)
            {
                int x = *q.begin();
                q.erase(q.begin());

                res += v[x];
                sz -= 2;

                if (q.find(l[x - 1]) == q.end())
                {
                    auto v = q.find(r[x] + 1);
                    if (v != q.end())
                        q.erase(v);
                }
                else if (q.find(r[x] + 1) == q.end())
                    q.erase(l[x - 1]);
                else
                {
                    q.erase(l[x - 1]);
                    q.erase(r[x] + 1);

                    l[r[r[x] + 1]] = l[x - 1];
                    r[l[x - 1]] = r[r[x] + 1];
                    v[l[x - 1]] = v[l[x - 1]] + v[r[x] + 1] - v[x];
                    q.insert(l[x - 1]);
                }
            }
            ans = min(ans, res);
        }

    cout << ans;
}

int32_t main()
{
    ios::sync_with_stdio(0);
    cin.tie(0);
    cout.tie(0);
    if (fopen(task ".INP", "r"))
    {
        freopen(task ".INP", "r", stdin);
        freopen(task ".OUT", "w", stdout);
    }
    Read();
    Sub_3();
}