/**
 * Author: 
 * Date: 2024-08-21
 * Description: Template C++ code
 */
#include <bits/stdc++.h> /** keep-include */
using namespace std;

#define rep(i, a, b) for (auto i = a; i < (b); ++i)
#define repr(i, a, b) for (auto i = (a) - 1; i >= (b); --i)
#define pb push_back
#define eb emplace_back
#define all(x) begin(x), end(x)
#define sz(x) int((x).size())
using ll = long long;
using pii = pair<int, int>;
using vi = vector<int>;
using vll = vector<ll>;
using vii = vector<pii>;

template<class T> inline bool cmax(T &a, const T &b)
{ return a < b ? a = b, 1 : 0; }
template<class T> inline bool cmin(T &a, const T &b)
{ return b < a ? a = b, 1 : 0; }

const int inf = 0x3f3f3f3f;
const ll linf = 1e18;
const double dinf = numeric_limits<double>::infinity();

template <class T> int sgn(T x) { return (x > 0) - (x < 0); }
template<class T>
struct Point {
	typedef Point P;
	T x, y;
	explicit Point(T x=0, T y=0) : x(x), y(y) {}
	bool operator<(P p) const { return tie(x,y) < tie(p.x,p.y); }
	bool operator==(P p) const { return tie(x,y)==tie(p.x,p.y); }
	P operator+(P p) const { return P(x+p.x, y+p.y); }
	P operator-(P p) const { return P(x-p.x, y-p.y); }
	P operator*(T d) const { return P(x*d, y*d); }
	P operator/(T d) const { return P(x/d, y/d); }
	T dot(P p) const { return x*p.x + y*p.y; }
	T cross(P p) const { return x*p.y - y*p.x; }
	T cross(P a, P b) const { return (a-*this).cross(b-*this); }
	T dist2() const { return x*x + y*y; }
	double dist() const { return sqrt((double)dist2()); }
	// angle to x-axis in interval [-pi, pi]
	double angle() const { return atan2(y, x); }
	P unit() const { return *this/dist(); } // makes dist()=1
	P perp() const { return P(-y, x); } // rotates +90 degrees
	P normal() const { return perp().unit(); }
	// returns point rotated 'a' radians ccw around the origin
	P rotate(double a) const {
		return P(x*cos(a)-y*sin(a),x*sin(a)+y*cos(a)); }
	friend ostream& operator<<(ostream& os, P p) {
		return os << "(" << p.x << "," << p.y << ")"; }
};

typedef Point<double> P;
bool circleInter(P a,P b,double r1,double r2,pair<P, P>* out) {
	if (a == b) { assert(r1 != r2); return false; }
	P vec = b - a;
	double d2 = vec.dist2(), sum = r1+r2, dif = r1-r2,
	       p = (d2 + r1*r1 - r2*r2)/(d2*2), h2 = r1*r1 - p*p*d2;
	if (sum*sum < d2 || dif*dif > d2) return false;
	P mid = a + vec*p, per = vec.perp() * sqrt(fmax(0, h2) / d2);
	*out = {mid + per, mid - per};
	return true;
}

double circleUnion(vector<P>& c, vector<double>& r) {
	double pi = acos(-1), a = 0;
	int n = sz(c);
	vi skip(n, 0);
	rep(i, 0, n) rep(j, 0, n)
		if (!skip[j] && j != i && sgn((c[j] - c[i]).dist() + r[i] - r[j]) <= 0) skip[i] = 1;
	rep(i, 0, n) if (!skip[i]) {
		vector<pair<double, double>> v;
		pair<P, P> p;
		int b = 0, m = 1;
		rep(j, 0, n) if (i != j && !skip[j] && circleInter(c[i], c[j], r[i], r[j], &p) && (p.first - p.second).dist() > 1e-8) {
			b = 1;
			double rs = (p.second - c[i]).angle(), rt = (p.first - c[i]).angle();
			if (rs < 0) rs += 2 * pi;
			if (rt < 0) rt += 2 * pi;
			if (rs < rt) v.pb({rs, rt});
			else v.pb({rs, 2 * pi}), v.pb({0, rt});
		}
		if (!b) { a += pi * r[i] * r[i]; continue; }
		sort(all(v));
		rep(j, 1, sz(v)) if (v[m - 1].second >= v[j].first) v[m - 1].second = max(v[m - 1].second, v[j].second); else v[m++] = v[j];
		v.pb({0, 0}), v[m] = v[0];
		rep(j, 0, m) {
			p.first = P(r[i], 0).rotate(v[j].second) + c[i];
			p.second = P(r[i], 0).rotate(v[j + 1].first) + c[i];
			a += p.first.cross(p.second) / 2;
			double ang = v[j + 1].first - v[j].second;
			if (ang < 0) ang += 2 * pi;
			a += 0.5 * r[i] * r[i] * (ang - sin(ang));
		}
	}
	return a;
}


int main() {
	cin.tie(0)->sync_with_stdio(0);
	cin.exceptions(cin.failbit);

    int n; double a;
    cin >> n >> a;

    vector<P> p(n);
    vector<double> t(n);
    rep(i, 0, n) {
        cin >> p[i].x >> p[i].y >> t[i];
    }

    double lo = 0, hi = 2e6;
    while (hi - lo > 1e-8) {
        double mid = (lo + hi) / 2;

        vector<double> r(n);
        rep(i, 0, n) {
            r[i] = max(0.0, mid - t[i]);
        }
        if (circleUnion(p, r) >= a) {
            hi = mid;
        } else {
            lo = mid;
        }
    }

    cout << fixed << setprecision(15) << lo << '\n';

	return 0;
}