Problem: 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}.

Examples

Input

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


Output

2.4


Input

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


Output

7411.2252

Solution (in CPP):

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

namespace geometry {
	using Real = double;
	using Point = complex<Real>;
	const Real EPS = 1e-9;
	const Real PI = acos(-1);
	struct Circle {
		Point p;
		Real r;
	};
	// 内積
	inline Real dot(const Point& lhs, const Point& rhs) {
		return (conj(lhs) * rhs).real();
	}
	// 外積
	inline Real cross(const Point& lhs, const Point& rhs) {
		return (conj(lhs) * rhs).imag();
	}
	// 円の交点
	vector<Point> intersect(const Circle& c1, const Circle& c2) {
		const Real dist = abs(c1.p - c2.p);
		vector<Point> ret;
		if(dist > c1.r + c2.r) return ret;
		if(dist < abs(c1.r - c2.r)) return ret;
		const Real rc = (dist * dist + c1.r * c1.r - c2.r * c2.r) / (2 * dist);
		const Real rs = sqrt(c1.r * c1.r - rc * rc);
		const Point vec = (c2.p - c1.p) / dist;
		ret.emplace_back(c1.p + vec * Point(rc, rs));
		ret.emplace_back(c1.p + vec * Point(rc, -rs));
		return ret;
	}

	inline istream& operator>>(istream& is, Point& p) {
		Real x, y;
		is >> x >> y;
		p = Point(x, y);
		return is;
	}
	inline ostream& operator<<(ostream& os, const Point &p) {
		return os << fixed << setprecision(10) << "(" << p.real() << ", " << p.imag() << ")";
	}
}


using namespace geometry;

int n, k;
Circle ci[60];
Real c[60];

bool bisearch(const Real d) {
	for(int i = 0; i < n; ++i) {
		ci[i].r = d / c[i];
	}
	vector<Point> pt;
	for(int i = 0; i < n; ++i) {
		pt.emplace_back(ci[i].p);
		for(int j = i + 1; j < n; ++j) {
			for(Point p : intersect(ci[i], ci[j])) {
				pt.emplace_back(p);
			}
		}
	}
	for(const Point& p : pt) {
		int cnt = 0;
		for(int i = 0; i < n; ++i) {
			if(c[i] * abs(p - ci[i].p) <= d + EPS) {
				++cnt;
			}
		}
		if(cnt >= k) return true;
	}
	return false;
}

int main() {
	cin >> n >> k;
	for(int i = 0; i < n; ++i) {
		cin >> ci[i].p >> c[i];
	}
	if(k == 1) {
		cout << 0 << '\n';
		return 0;
	}
	Real ok = 1e18, ng = -1e-18;
	int cnt = 100;
	while(cnt--) {
		const Real mid = (ok + ng) / 2;
		if(bisearch(mid)) {
			ok = mid;
		} else {
			ng = mid;
		}
	}
	printf("%.15f\n", ok);
	return 0;
}