Mr. Chanek lives in a city represented as a plane. He wants to build an amusement park in the shape of a circle of radius r. The circle must touch the origin (point (0, 0)).

There are n bird habitats that can be a photo spot for the tourists in the park. The i-th bird habitat is at point p_i = (x_i, y_i). 

Find the minimum radius r of a park with at least k bird habitats inside. 

A point is considered to be inside the park if and only if the distance between p_i and the center of the park is less than or equal to the radius of the park. Note that the center and the radius of the park do not need to be integers.

In this problem, it is guaranteed that the given input always has a solution with r ≤ 2 ⋅ 10^5.

Input

The first line contains two integers n and k (1 ≤ n ≤ 10^5, 1 ≤ k ≤ n) — the number of bird habitats in the city and the number of bird habitats required to be inside the park.

The i-th of the next n lines contains two integers x_i and y_i (0 ≤ |x_i|, |y_i| ≤ 10^5) — the position of the i-th bird habitat.

Output

Output a single real number r denoting the minimum radius of a park with at least k bird habitats inside. It is guaranteed that the given input always has a solution with r ≤ 2 ⋅ 10^5.

Your answer is considered correct if its absolute or relative error does not exceed 10^{-4}.

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^{-4}.

Examples

Input


8 4
-3 1
-4 4
1 5
2 2
2 -2
-2 -4
-1 -1
-6 0


Output


3.1622776589


Input


1 1
0 0


Output


0.0000000000

Note

In the first example, Mr. Chanek can put the center of the park at (-3, -1) with radius √{10} ≈ 3.162. It can be proven this is the minimum r.

The following illustrates the first example. The blue points represent bird habitats and the red circle represents the amusement park.

<image>
#include <bits/stdc++.h>
#pragma GCC optimize("Ofast")
using namespace std;
void yes() {
  cout << "YES\n";
  return;
}
void no() {
  cout << "NO\n";
  return;
}
template <class T>
void out(T temp) {
  cout << temp << endl;
  return;
}
void out(double temp) {
  cout << setprecision(7) << fixed << temp << endl;
  return;
}
void out(long double temp) {
  cout << setprecision(7) << fixed << temp << endl;
  return;
}
struct pt {
  int x, y;
  long double deg;
};
const long double PI = 3.14159265358979323846, ep = 1e-6;
void init() {}
long double dist(long double a, long double b) { return sqrt(a * a + b * b); }
long double find_deg(long double x, long double y) {
  if (x == 0 && y == 0) {
    return -1;
  }
  if (x > 0 && y == 0) {
    return 0;
  }
  if (x > 0 && y > 0) {
    return atan2(abs(y), abs(x)) / PI * 180;
  } else if (x == 0 && y > 0) {
    return 90;
  } else if (x < 0 && y > 0) {
    return 90 + atan2(abs(x), abs(y)) / PI * 180;
  } else if (x < 0 && y == 0) {
    return 180;
  } else if (x < 0 && y < 0) {
    return 180 + atan2(abs(y), abs(x)) / PI * 180;
  } else if (x == 0 && y < 0) {
    return 270;
  } else if (x > 0 && y < 0) {
    return 270 + atan2(abs(x), abs(y)) / PI * 180;
  } else {
    cout << "GO DEBUG HAHAHAHAHAHAHAHA\n";
  }
  return -2;
}
void solve(int case_no) {
  int n, k;
  cin >> n >> k;
  vector<pt> v;
  for (int i = 0; i < n; i++) {
    pt cur;
    cin >> cur.x >> cur.y;
    cur.deg = find_deg(cur.x, cur.y);
    if (cur.deg == -2) {
      cout << "wrong smh\n";
      while (true) continue;
      return;
    } else if (cur.deg == -1) {
      k--;
    } else {
      v.push_back(cur);
    }
  }
  if (k <= 0) return out("0.00000000");
  n = v.size();
  cout << setprecision(8) << fixed;
  long double lb = 0, rb = dist(1e5, 1e5);
  int turns = 50;
  while (turns--) {
    long double mid = (lb + rb) / 2;
    priority_queue<pair<long double, bool>, vector<pair<long double, bool> >,
                   greater<pair<long double, bool> > >
        pq;
    for (int i = 0; i < n; i++) {
      if (dist(v[i].x, v[i].y) > 2 * mid) continue;
      pt cen;
      if (true) {
        long double s = 2 * mid + dist(v[i].x, v[i].y);
        long double area =
            sqrt(s * (s - mid) * (s - mid) * (s - dist(v[i].x, v[i].y)));
        long double midpt_dist = area / dist(v[i].x, v[i].y);
        pt midpt;
        midpt.x = v[i].x / 2.0;
        midpt.y = v[i].y / 2.0;
        long double slope = v[i].y * 1.0 / v[i].x;
        slope = -1.0 / slope;
        long double deltax =
            sqrt((midpt_dist * midpt_dist) / (slope * slope + 1));
        cen.x = midpt.x + deltax;
        cen.y = midpt.y + (slope * deltax);
        cen.deg = find_deg(cen.x, cen.y);
        long double reflect_deg =
            (atan2(midpt_dist, (dist(v[i].x, v[i].y) / 2.0))) / PI * 180;
        if (find_deg(cen.x, cen.y) < find_deg(v[i].x, v[i].y)) {
          pq.push({cen.deg, true});
          pq.push({cen.deg + 360, true});
          pq.push({cen.deg + reflect_deg * 2, false});
          pq.push({cen.deg + reflect_deg * 2 + 360, false});
        } else {
          pq.push({cen.deg, false});
          pq.push({cen.deg + 360, false});
          pq.push({cen.deg - reflect_deg * 2, true});
          pq.push({cen.deg - reflect_deg * 2 + 360, true});
        }
      }
    }
    long double prev = -1;
    int cnt = 0, best = 0;
    cout << "mid = " << mid << endl;
    while (!pq.empty()) {
      pair<long double, bool> cur = pq.top();
      pq.pop();
      cout << cur.first << ' ' << cur.second << endl;
      if (abs(cur.first - prev) > ep) {
        best = max(best, cnt);
      }
      prev = cur.first;
      if (cur.second)
        cnt++;
      else
        cnt--;
    }
    if (best >= k)
      rb = mid;
    else
      lb = mid;
  }
  cout << setprecision(6) << fixed << lb * 2 << endl;
}
int main() {
  ios::sync_with_stdio(false);
  cin.tie(NULL);
  cout.tie(NULL);
  srand(time(NULL));
  init();
  int t = 1;
  for (int i = 1; i <= t; i++) solve(i);
}
