#include <bits/stdc++.h>
using namespace std;

using ll = long long;
using lll = __int128;
const int MXN = 50005;
const char BAS = 'a';
const int CHST = 26;
const int MXD = MXN * 2;
int N, K;
char str[MXN];
ll L(-1), R(1e18 + 105), diff[MXN];
int nxt[MXD][CHST], fail[MXD], len[MXD], fir[MXD], lst[MXD];
vector<int> son[MXD];

void dfs(int p) {
  for (int q : son[p])
    dfs(q), fir[p] = min(fir[p], fir[q]), lst[p] = max(lst[p], lst[q]);
}
lll calcv(int l, int r) {
  int slen(r - l), ndsz(0);
  static auto newnode = [&]() {
    int p(++ndsz);
    memset(nxt[p], 0, sizeof nxt[p]);
    son[p].clear();
    fir[p] = slen + 1, lst[p] = 0;
    return p;
  };
  int n(newnode());
  fail[n] = 0, len[n] = 0;
  for (int i(l); i != r; ++i) {
    int c(str[i]);
    int t(n);
    int p(n = newnode());
    fir[p] = lst[p] = i - l + 1;
    len[p] = len[t] + 1;
    while (t && !nxt[t][c]) nxt[t][c] = p, t = fail[t];
    if (!t) {
      fail[p] = 1;
      continue;
    }
    int f(nxt[t][c]);
    if (len[f] == len[t] + 1) {
      fail[p] = f;
      continue;
    }
    int a(newnode());
    len[a] = len[t] + 1;
    fail[a] = fail[f], fail[f] = fail[p] = a;
    memcpy(nxt[a], nxt[f], sizeof nxt[a]);
    while (t && nxt[t][c] == f) nxt[t][c] = a, t = fail[t];
  }

  for (int i(2); i <= ndsz; ++i) son[fail[i]].push_back(i);
  dfs(1);
  auto add = [](int l, int r, int s, int v) {
    s = min(s, r - l);
    diff[l] += s * v;
    diff[l + 1] -= s * v;
    diff[r - s + 1] -= v;
    diff[r + 1] += v;
//  cout << l << '+' << s * v << ';';
//  cout << l + 1 << '-' << s * v << ';';
//  cout << r - s + 1 << '-' << v << ';';
//  cout << r + 1 << '+' << v << ';' << endl;
  };
  for (int i(0); i <= slen; ++i) diff[i] = 0;
  for (int i(2); i <= ndsz; ++i) {
    add(fir[i], lst[i], len[i], 1);
    add(fir[i], lst[i], len[fail[i]], -1);
  }
  for (int i(1); i <= slen; ++i) diff[i] += diff[i - 1];
  lll v(0);
  ll w(0);
  for (int i(0); i <= slen; ++i) {
    w += diff[i];
//  cout << w << ',';
    v += static_cast<lll>(w) * w;
  }
//cout << endl;
  return v;
}

int calcp(ll lim) {
  int cnt(0);
  for (int i(0); i != N; ++cnt) {
    int plen(1);
    while (i + (plen <<= 1) <= N)
      if (calcv(i, i + plen) > lim) break;
    plen >>= 1;
    for (int d(plen >> 1); d; d >>= 1)
      if (i + plen + d <= N && calcv(i, i + plen + d) <= lim)
        plen += d;
//  cout << lim << ':' << i << ':' << plen << endl;
    i += plen;
  }
  return cnt;
}

int main() {
  cin >> N >> K >> str;
  for (int i(0); i != N; ++i) str[i] -= BAS;
  while (R - L > 1) {
    ll mid((L + R) >> 1);
    if (calcp(mid) <= K) R = mid;
    else L = mid;
  }
  cout << R << endl;
  return 0;
}