Problem:
Score : 600 points

Problem Statement

Takahashi wants to grill N pieces of meat on a grilling net, which can be seen as a two-dimensional plane. The coordinates of the i-th piece of meat are \left(x_i, y_i\right), and its hardness is c_i.

Takahashi can use one heat source to grill the meat. If he puts the heat source at coordinates \left(X, Y\right), where X and Y are real numbers, the i-th piece of meat will be ready to eat in c_i \times \sqrt{\left(X - x_i\right)^2 + \left(Y-y_i\right)^2} seconds.

Takahashi wants to eat K pieces of meat. Find the time required to have K or more pieces of meat ready if he put the heat source to minimize this time.

Constraints

All values in input are integers.

1 \leq N \leq 60

1 \leq K \leq N

-1000 \leq x_i , y_i \leq 1000

\left(x_i, y_i\right) \neq \left(x_j, y_j\right) \left(i \neq j \right)

1 \leq c_i \leq 100

Input

Input is given from Standard Input in the following format:

N K
x_1 y_1 c_1
\vdots
x_N y_N c_N

Output

Print the answer.

It will be considered correct if its absolute or relative error from our answer is at most 10^{-6}.

Sample Input 1

4 3
-1 0 3
0 0 3
1 0 2
1 1 40

Sample Output 1

2.4

If we put the heat source at \left(-0.2, 0\right), the 1-st, 2-nd, and 3-rd pieces of meat will be ready to eat within 2.4 seconds. This is the optimal place to put the heat source.

Sample Input 2

10 5
-879 981 26
890 -406 81
512 859 97
362 -955 25
128 553 17
-885 763 2
449 310 57
-656 -204 11
-270 76 40
184 170 16

Sample Output 2

7411.2252

Solution in C++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

#define _CRT_SECURE_NO_WARNINGS

#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <cmath>
#include <limits>
#include <ctime>
#include <cassert>
#include <map>
#include <set>
#include <iostream>
#include <memory>
#include <string>
#include <vector>
#include <algorithm>
#include <functional>
#include <sstream>
#include <stack>
#include <queue>
#include <numeric>
#include <iterator>
#include <bitset>
#include <unordered_map>
#include <unordered_set>

using namespace std;
#define FOR(i,n) for(int i = 0; i < (n); i++)
#define sz(c) ((int)c.size())
#define ten(n) ((int)1e##n)
using ll = long long;
using Pii = pair<int, int>;
using Pll = pair<ll, ll>;

template<typename ...> static inline int getchar_unlocked(void) { return getchar(); }
template<typename ...> static inline void putchar_unlocked(int c) { putchar(c); }
#define mygc(c) (c)=getchar_unlocked()
#define mypc(c) putchar_unlocked(c)
void reader(int& x) { int k, m = 0; x = 0; for (;;) { mygc(k); if (k == '-') { m = 1; break; }if ('0' <= k && k <= '9') { x = k - '0'; break; } }for (;;) { mygc(k); if (k<'0' || k>'9')break; x = x * 10 + k - '0'; }if (m) x = -x; }
void reader(ll& x) { int k, m = 0; x = 0; for (;;) { mygc(k); if (k == '-') { m = 1; break; }if ('0' <= k && k <= '9') { x = k - '0'; break; } }for (;;) { mygc(k); if (k<'0' || k>'9')break; x = x * 10 + k - '0'; }if (m) x = -x; }
int reader(char c[]) { int i, s = 0; for (;;) { mygc(i); if (i != ' ' && i != '\n' && i != '\r' && i != '\t' && i != EOF) break; }c[s++] = i; for (;;) { mygc(i); if (i == ' ' || i == '\n' || i == '\r' || i == '\t' || i == EOF) break; c[s++] = i; }c[s] = '\0'; return s; }
int reader(string& c) { int i; for (;;) { mygc(i); if (i != ' ' && i != '\n' && i != '\r' && i != '\t' && i != EOF) break; }c.push_back(i); for (;;) { mygc(i); if (i == ' ' || i == '\n' || i == '\r' || i == '\t' || i == EOF) break; c.push_back(i); }; return sz(c); }
template <class T, class S> void reader(T& x, S& y) { reader(x); reader(y); }
template <class T, class S, class U> void reader(T& x, S& y, U& z) { reader(x); reader(y); reader(z); }
template <class T, class S, class U, class V> void reader(T& x, S& y, U& z, V& w) { reader(x); reader(y); reader(z); reader(w); }
void writer(int x, char c) { int s = 0, m = 0; char f[10]; if (x < 0)m = 1, x = -x; while (x)f[s++] = x % 10, x /= 10; if (!s)f[s++] = 0; if (m)mypc('-'); while (s--)mypc(f[s] + '0'); mypc(c); }
void writer(ll x, char c) { int s = 0, m = 0; char f[20]; if (x < 0)m = 1, x = -x; while (x)f[s++] = x % 10, x /= 10; if (!s)f[s++] = 0; if (m)mypc('-'); while (s--)mypc(f[s] + '0'); mypc(c); }
void writer(const char c[]) { int i; for (i = 0; c[i] != '\0'; i++)mypc(c[i]); }
void writer(const string& x, char c) { int i; for (i = 0; x[i] != '\0'; i++)mypc(x[i]); mypc(c); }
void writer(const char x[], char c) { int i; for (i = 0; x[i] != '\0'; i++)mypc(x[i]); mypc(c); }
template<class T> void writerLn(T x) { writer(x, '\n'); }
template<class T, class S> void writerLn(T x, S y) { writer(x, ' '); writer(y, '\n'); }
template<class T, class S, class U> void writerLn(T x, S y, U z) { writer(x, ' '); writer(y, ' '); writer(z, '\n'); }
template<class T, class S, class U, class V> void writerLn(T x, S y, U z, V v) { writer(x, ' '); writer(y, ' '); writer(z, ' '); writer(v, '\n'); }
template<class T> void writerArr(T x[], int n) { if (!n) { mypc('\n'); return; }FOR(i, n - 1)writer(x[i], ' '); writer(x[n - 1], '\n'); }
template<class T> void writerArr(vector<T>& x) { writerArr(x.data(), (int)x.size()); }

template<class T> void chmin(T& a, const T& b) { if (a > b) a = b; }
template<class T> void chmax(T& a, const T& b) { if (a < b) a = b; }

template<class T> T gcd(T a, T b) { return b ? gcd(b, a % b) : a; }
template<class T> T lcm(T a, T b) { return a / gcd(a, b) * b; }
ll mod_pow(ll a, ll n, ll mod) {
	ll ret = 1;
	ll p = a % mod;
	while (n) {
		if (n & 1) ret = ret * p % mod;
		p = p * p % mod;
		n >>= 1;
	}
	return ret;
}
template<class T> T extgcd(T a, T b, T& x, T& y) { for (T u = y = 1, v = x = 0; a;) { T q = b / a; swap(x -= q * u, u); swap(y -= q * v, v); swap(b -= q * a, a); } return b; }
ll mod_inv(ll a, ll m) { ll x, y; extgcd<ll>(a, m, x, y); return (m + x % m) % m; }

#ifdef _MSC_VER
// #ifdef _DEBUG
template <typename ... Args>
void debugPrintf(const char* format, Args const& ... args) {
	fprintf(stderr, format, args ...);
	fflush(stderr);
}
#else
#define debugPrintf(...)
#endif

using T = double;

struct P {
	T x, y;
	P() : x(0), y(0) {}
	P(const T& x, const T& y) : x(x), y(y) {}
	P operator+(const P& a)const { return P(x + a.x, y + a.y); }
	P& operator+=(const P& a) { x += a.x; y += a.y; return *this; }
	P operator-(const P& a)const { return P(x - a.x, y - a.y); }
	P& operator-=(const P& a) { x -= a.x; y -= a.y; return *this; }
	P operator*(const T a)const { return P(a * x, a * y); }
	P& operator*=(const T a) { x *= a; y *= a; return *this; }
	P operator/(const T a)const { return P(x / a, y / a); }
	P& operator/=(const T a) { x /= a; y /= a; return *this; }

	//比較用
	bool operator<(const P& a)const { return (x != a.x) ? (x < a.x) : (y < a.y); }
};

T SQ(T x) { return x * x; }
T abs2(const P& p) { return SQ(p.x) + SQ(p.y); }
T abs(const P& p) { return sqrt(abs2(p)); }

struct C {
	P c;
	T r;
	C() {}
	C(const P& c, T r) : c(c), r(r) {}
};
const double EPS = 1e-9;

int intersect(const C& C1, const C& C2, P* p = NULL, P* q = NULL) {
	double r1 = C1.r, r2 = C2.r;
	P p1 = C1.c, p2 = C2.c;

	double d = abs(p1 - p2);
	if (d < EPS && abs(r1 - r2) < EPS) { // C1==C2
		return -1;
	} else if (r1 + r2 < d - EPS || d + EPS < abs(r1 - r2)) {
		return 0;
	} else {
		double a = (r1 * r1 - r2 * r2 + d * d) / (2 * d);
		double h = sqrt(max(r1 * r1 - a * a, 0.0));
		P tmp1 = p1 + (p2 - p1) * a / d;
		P tmp2 = (p2 - p1) * h / d;
		if (abs(tmp2) < EPS) {
			if (p && q) *p = *q = tmp1;
			return 1;
		} else {
			if (p && q) {
				*p = P(tmp1.x - tmp2.y, tmp1.y + tmp2.x);
				*q = P(tmp1.x + tmp2.y, tmp1.y - tmp2.x);
			}
			return 2;
		}
	}
}

int main() {
	int n, k; reader(n, k);
	vector<tuple<int,int,int>> vp;
	
	FOR(i, n) {
		int a, b, c; reader(a, b, c);
		vp.emplace_back(a, b, c);
	}

	double l = 0, r = 3e5;
	FOR(_, 150) {
		double md = (l + r) / 2;
		vector<C> vpc;
		for (auto& abc : vp) {
			int a, b, c; tie(a, b, c) = abc;
			vpc.push_back(C(P(a, b), md / c));
		}
		vector<P> ps;
		FOR(i, n) FOR(j, i) {
			P p, q;
			int cnt = intersect(vpc[i], vpc[j], &p, &q);
			if (cnt >= 1) ps.push_back(p);
			if (cnt >= 2) ps.push_back(q);
		}
		bool ok = false;
		for (auto p : ps) {
			int cnt = 0;
			for (auto c : vpc) {
				double dist2 = abs2(p - c.c);
				double dd = c.r* c.r;
				if (dist2 / dd <= 1 + EPS) cnt++;
			}
			if (cnt >= k) ok = true;
		}
		if (ok) r = md;
		else l = md;
	}
	if (k == 1) l = 0;
	printf("%.10lf\n", l);


	return 0;
}