Problem: You are given an integer k and n distinct points with integer coordinates on the Euclidean plane, the i-th point has coordinates (x_i, y_i).

Consider a list of all the (n(n - 1))/(2) pairs of points ((x_i, y_i), (x_j, y_j)) (1 ≤ i < j ≤ n). For every such pair, write out the distance from the line through these two points to the origin (0, 0).

Your goal is to calculate the k-th smallest number among these distances.

Input

The first line contains two integers n, k (2 ≤ n ≤ 10^5, 1 ≤ k ≤ (n(n - 1))/(2)).

The i-th of the next n lines contains two integers x_i and y_i (-10^4 ≤ x_i, y_i ≤ 10^4) — the coordinates of the i-th point. It is guaranteed that all given points are pairwise distinct.

Output

You should output one number — the k-th smallest distance from the origin. Your answer is considered correct if its absolute or relative error does not exceed 10^{-6}.

Formally, let your answer be a, and the jury's answer be b. Your answer is accepted if and only if \frac{|a - b|}{max{(1, |b|)}} ≤ 10^{-6}.

Example

Input


4 3
2 1
-2 -1
0 -1
-2 4


Output


0.707106780737

Note

There are 6 pairs of points: 

  * Line 1-2 : distance 0 from the origin 
  * Line 1-3 : distance \frac{√{2}}{2} ≈ 0.707106781 from the origin 
  * Line 1-4 : distance 2 from the origin 
  * Line 2-3 : distance 1 from the origin 
  * Line 2-4 : distance 2 from the origin 
  * Line 3-4 : distance \frac{2}{√{29}} ≈ 0.371390676 from the origin 

The third smallest distance among those is approximately 0.707106781.

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
template <class t, class u>
void chmax(t& first, u second) {
  if (first < second) first = second;
}
template <class t, class u>
void chmin(t& first, u second) {
  if (second < first) first = second;
}
template <class t>
using vc = vector<t>;
template <class t>
using vvc = vc<vc<t>>;
using pi = pair<ll, ll>;
using vi = vc<ll>;
template <class t, class u>
ostream& operator<<(ostream& os, const pair<t, u>& p) {
  return os << "{" << p.first << "," << p.second << "}";
}
template <class t>
ostream& operator<<(ostream& os, const vc<t>& v) {
  os << "{";
  for (auto e : v) os << e << ",";
  return os << "}";
}
using uint = unsigned;
using ull = unsigned long long;
template <class t, size_t n>
ostream& operator<<(ostream& os, const array<t, n>& first) {
  return os << vc<t>(first.begin(), first.end());
}
template <ll i, class T>
void print_tuple(ostream&, const T&) {}
template <ll i, class T, class H, class... Args>
void print_tuple(ostream& os, const T& t) {
  if (i) os << ",";
  os << get<i>(t);
  print_tuple<i + 1, T, Args...>(os, t);
}
template <class... Args>
ostream& operator<<(ostream& os, const tuple<Args...>& t) {
  os << "{";
  print_tuple<0, tuple<Args...>, Args...>(os, t);
  return os << "}";
}
template <class t>
void print(t x, ll suc = 1) {
  cout << x;
  if (suc == 1) cout << "\n";
  if (suc == 2) cout << " ";
}
ll read() {
  ll i;
  cin >> i;
  return i;
}
vi readvi(ll n, ll off = 0) {
  vi v(n);
  for (ll i = ll(0); i < ll(n); i++) v[i] = read() + off;
  return v;
}
pi readpi(ll off = 0) {
  ll first, second;
  cin >> first >> second;
  return pi(first + off, second + off);
}
template <class T>
void print(const vector<T>& v, ll suc = 1) {
  for (ll i = ll(0); i < ll(v.size()); i++)
    print(v[i], i == ll(v.size()) - 1 ? suc : 2);
}
string readString() {
  string s;
  cin >> s;
  return s;
}
template <class T>
T sq(const T& t) {
  return t * t;
}
void yes(bool ex = true) {
  cout << "Yes"
       << "\n";
  if (ex) exit(0);
}
void no(bool ex = true) {
  cout << "No"
       << "\n";
  if (ex) exit(0);
}
void possible(bool ex = true) {
  cout << "Possible"
       << "\n";
  if (ex) exit(0);
}
void impossible(bool ex = true) {
  cout << "Impossible"
       << "\n";
  if (ex) exit(0);
}
constexpr ll ten(ll n) { return n == 0 ? 1 : ten(n - 1) * 10; }
const ll infLL = LLONG_MAX / 3;
const ll inf = infLL;
ll topbit(signed t) { return t == 0 ? -1 : 31 - __builtin_clz(t); }
ll topbit(ll t) { return t == 0 ? -1 : 63 - __builtin_clzll(t); }
ll botbit(signed first) { return first == 0 ? 32 : __builtin_ctz(first); }
ll botbit(ll first) { return first == 0 ? 64 : __builtin_ctzll(first); }
ll popcount(signed t) { return __builtin_popcount(t); }
ll popcount(ll t) { return __builtin_popcountll(t); }
bool ispow2(ll i) { return i && (i & -i) == i; }
ll mask(ll i) { return (ll(1) << i) - 1; }
bool inc(ll first, ll second, ll c) { return first <= second && second <= c; }
template <class t>
void mkuni(vc<t>& v) {
  sort(v.begin(), v.end());
  v.erase(unique(v.begin(), v.end()), v.end());
}
ll rand_int(ll l, ll r) {
  static mt19937_64 gen(chrono::steady_clock::now().time_since_epoch().count());
  return uniform_int_distribution<ll>(l, r)(gen);
}
template <class t>
void myshuffle(vc<t>& first) {
  for (ll i = ll(0); i < ll(ll(first.size())); i++)
    swap(first[i], first[rand_int(0, i)]);
}
template <class t>
ll lwb(const vc<t>& v, const t& first) {
  return lower_bound(v.begin(), v.end(), first) - v.begin();
}
vvc<ll> readGraph(ll n, ll m) {
  vvc<ll> g(n);
  for (ll i = ll(0); i < ll(m); i++) {
    ll first, second;
    cin >> first >> second;
    first--;
    second--;
    g[first].push_back(second);
    g[second].push_back(first);
  }
  return g;
}
vvc<ll> readTree(ll n) { return readGraph(n, n - 1); }
template <class t>
struct BIT {
  vc<t> buf;
  ll s;
  BIT(ll n = 0) { init(n); }
  void init(ll n) { buf.assign(s = n, 0); }
  void add(ll i, t v) {
    for (; i < s; i += (i + 1) & (-i - 1)) buf[i] += v;
  }
  t get(ll i) {
    t res = 0;
    for (; i >= 0; i -= (i + 1) & (-i - 1)) res += buf[i];
    return res;
  }
  t sum(ll second, ll e) { return get(e - 1) - get(second - 1); }
  ll kth(ll k) {
    ll res = 0;
    for (ll i = topbit(s); i >= 0; i--) {
      ll w = res + (1 << i);
      if (w <= s && buf[w - 1] <= k) {
        k -= buf[w - 1];
        res = w;
      }
    }
    return res;
  }
  ll kth_helper(ll k, ll i) { return kth(k + get(i - 1)); }
};
using ld = double;
using P = pair<ld, ld>;
const ld PI = acos(ld(-1));
bool dbg;
ll sub(vc<P> ps, const ld r) {
  ll n = ll(ps.size());
  ll res = 0;
  vc<P> w;
  for (auto p : ps) {
    ld d = acos(min(r / p.first, ld(1)));
    ld lw = p.second - d, up = p.second + d;
    if (lw < -PI) lw += 2 * PI;
    if (PI < up) up -= 2 * PI;
    if (lw > up) swap(lw, up);
    w.emplace_back(lw, up);
  }
  sort(w.begin(), w.end());
  if (dbg) {
    void(0);
  }
  vc<ld> xs(ll(w.size()));
  for (ll i = ll(0); i < ll(ll(w.size())); i++) xs[i] = w[i].first;
  vc<ld> ys(ll(w.size()));
  for (ll i = ll(0); i < ll(ll(w.size())); i++) ys[i] = w[i].second;
  sort(ys.begin(), ys.end());
  BIT<ll> bit(n), bit2(n);
  for (ll i = ll(ll(w.size())) - 1; i >= ll(0); i--) {
    {
      ll j = lwb(ys, w[i].second);
      res += bit.get(j);
      bit.add(j, 1);
    }
    {
      ll j = lwb(xs, w[i].second) - 1;
      res += n - 1 - i - bit2.get(j);
    }
    {
      ll j = lwb(xs, w[i].first);
      bit2.add(j, 1);
    }
  }
  return res;
}
void slv() {
  ll n, k;
  cin >> n >> k;
  k--;
  ld lw = 0, up = 15000;
  vc<P> ps(n);
  for (ll i = ll(0); i < ll(n); i++) {
    P p;
    cin >> p.first >> p.second;
    ps[i] = P(sqrt(sq(p.first) + sq(p.second)), atan2(p.second, p.first));
  }
  for (ll _ = ll(0); _ < ll(45); _++) {
    const ld mid = (lw + up) / 2;
    vc<P> tmp;
    for (auto p : ps) {
      if (p.first > mid) {
        tmp.push_back(p);
      }
    }
    ll rem = n - ll(tmp.size());
    ll cnt = ll(tmp.size()) * rem + rem * (rem - 1) / 2;
    if (cnt <= k) cnt += sub(tmp, mid);
    if (cnt <= k)
      lw = mid;
    else
      up = mid;
  }
  cout << up << endl;
}
signed main() {
  cin.tie(0);
  ios::sync_with_stdio(0);
  cout << fixed << setprecision(20);
  slv();
}