///////////////////////////////////////////////////////////////////////////////

#include <bits/stdc++.h>
#include <unistd.h>
#include <time.h>
#include <sys/time.h>

using namespace std;

///////////////////////////////////////////////////////////////////////////////

#define DEBUG 0

#define pb push_back
#define V vector
#define M unordered_map
#define S static

#define rep(i,n) for(ll i=0LL; i<n; ++i)
#define srep(i,s,n) for(ll i=s; i<n; ++i)
#define rrep(i,n) for(ll i=n-1LL; i>=0LL; --i)
#define ALL(a) (a).begin(),(a).end()
#define RALL(a) (a).rbegin(),(a).rend()
#define CIN(x) do { \
        assert(!cin.eof()); \
        cin >> x; \
        assert(!cin.fail()); \
} while(0);
#if DEBUG
#define debug_print(...) _debug_print(__VA_ARGS__)
#define debug_printf(...) printf(__VA_ARGS__)
#define debug_print_time _debug_print_time
#else // DEBUG
#define debug_print(...)
#define debug_printf(...)
#define debug_print_time
#endif // DEBUG

typedef long long ll;
typedef unsigned long long ull;
typedef tuple<ll, ll> t2;
typedef tuple<ll, ll, ll> t3;
typedef tuple<ll, ll, ll, ll> t4;
typedef tuple<ll, ll, ll, ll, ll> t5;
template <typename T>
using priority_queue_incr = priority_queue<T, V<T>, greater<T> >;

///////////////////////////////////////////////////////////////////////////////

template <typename TT, typename T>
T get_m(M<TT, T> &m, TT k, T default_value)
{
    if (m.find(k) == m.end()) return m[k] = default_value;
    return m[k];
}

template <typename TT, typename T>
void incr_m(M<TT, T> &m, TT k)
{
    if (m.find(k) == m.end()) m[k] = 0;
    m[k]++;
}

template <typename TT, typename T>
void incr_m(map<TT, T> &m, TT k)
{
    if (m.find(k) == m.end()) m[k] = 0;
    m[k]++;
}

void llin(ll &a)
{
    CIN(a);
}

void llinl1(V<ll> &v, ll count)
{
    for (ll i = 0LL; i < count; ++i) {
        ll a;
        CIN(a);
        v.push_back(a);
    }
}

void llinl2(V<t2> &v, ll count)
{
    for (ll i = 0LL; i < count; ++i) {
        ll a, b;
        CIN(a >> b);
        v.push_back(t2(a, b));
    }
}

void llinl3(V<t3> &v, ll count)
{
    for (ll i = 0LL; i < count; ++i) {
        ll a, b, c;
        CIN(a >> b >> c);
        v.push_back(t3(a, b, c));
    }
}

void llinl4(V<t4> &v, ll count)
{
    for (ll i = 0LL; i < count; ++i) {
        ll a, b, c, d;
        CIN(a >> b >> c >> d);
        v.push_back(t4(a, b, c, d));
    }
}

void llina(V<ll> &v, ll count)
{
    llinl1(v, count);
}

template <typename T>
void sort(V<T> &v)
{
    sort(v.begin(), v.end());
}

template <typename T>
void sort_reverse(V<T> &v)
{
    sort(v.begin(), v.end(), greater<T>());
}

template <typename T>
void _debug_print(T x)
{
    cout << x << endl;
}

void _debug_print(const t2 &x)
{
    ll x1 = get<0>(x);
    ll x2 = get<1>(x);
    cout << "-- " << x1 << " -- " << x2 << endl;
}

void _debug_print(const t3 &x)
{
    ll x1 = get<0>(x);
    ll x2 = get<1>(x);
    ll x3 = get<2>(x);
    cout << "-- " << x1 << " -- " << x2 << " -- " << x3 << endl;
}

void _debug_print(const t4 &x)
{
    ll x1 = get<0>(x);
    ll x2 = get<1>(x);
    ll x3 = get<2>(x);
    ll x4 = get<3>(x);
    cout << "-- " << x1 << " -- " << x2
         << " -- " << x3 << " -- " << x4 << endl;
}

template <typename T>
void _debug_print(T xarray[], ll n)
{
    rep (i, n) _debug_print(xarray[i]);
}

template <typename T>
void _debug_print(const V<T> &xlist)
{
    for (auto x : xlist) {
        cout << "-- ";
        _debug_print(x);
    }
}

template <typename T>
void _debug_print(const set<T> &xset)
{
    for (auto x : xset) {
        cout << "-- ";
        _debug_print(x);
    }
}

template <typename TT, typename T>
void _debug_print(const M<TT, T> &xlist)
{
    for (auto x : xlist) {
        TT k = x.first;
        T v = x.second;
        cout << "====" << endl;
        cout << "K=";
        _debug_print(k);
        cout << "V=";
        _debug_print(v);
    }
}

template <typename TT, typename T>
void _debug_print(const map<TT, T> &xlist)
{
    for (auto x : xlist) {
        TT k = x.first;
        T v = x.second;
        cout << "====" << endl;
        cout << "K=";
        _debug_print(k);
        cout << "V=";
        _debug_print(v);
    }
}

void _debug_print_time(const char *prefix)
{
    struct timeval tv;
    gettimeofday(&tv, NULL);
#if DEBUG
    struct tm *tm = localtime(&tv.tv_sec);
#endif
    debug_printf("-- %s %02d:%02d:%02d.%06ld\n",
                 prefix, tm->tm_hour, tm->tm_min, tm->tm_sec, tv.tv_usec);
}

///////////////////////////////////////////////////////////////////////////////

void _main();
int main()
{
    cout << setprecision(12);
#if !DEBUG
    ios::sync_with_stdio(false);
    cin.tie(0);
#endif

    _main();
    return 0;
}

typedef tuple<double, double> tdd;
ll nnnn;

bool solve(V<tdd> &res, double cx1, double cy1, double r1,
           double cx2, double cy2, double r2)
{
    assert(cy1 != cy2);

    double xx = cx1 * cx1 + cy1 * cy1;
    double yy = cx2 * cx2 + cy2 * cy2;
    double zz = xx - yy - r1 * r1 + r2 * r2;
    double kk = -(cx1 - cx2) / (cy1 - cy2);
    double ww = zz / (2. * (cy1 - cy2));
    double ff = ww - cy1;
    double mm = cx1 * cx1 + ff * ff - r1 * r1;
    double inroot = (cx1 - kk * ff) * (cx1 - kk * ff) - (kk * kk + 1.) * mm;

    if (nnnn == 2) debug_printf("inroot=%lf\n", inroot);

    if (inroot < 0.) return false;

    double root = sqrt(inroot);
    root /= kk * kk + 1.;

    double x_base = cx1 - kk * ff;
    x_base /= kk * kk + 1.;

    if (nnnn == 2) debug_printf("xx=%lf yy=%lf ff=%lf\n", xx, yy, ff);
    if (nnnn == 2) debug_printf("zz=%lf kk=%lf ww=%lf x_base=%lf\n", zz, kk, ww, x_base);

    double x1 = x_base + root;
    double x2 = x_base - root;
    double y1 = kk * x1 + ww;
    double y2 = kk * x2 + ww;

    res.pb(tdd(x1, y1));
    res.pb(tdd(x2, y2));
    return true;
}

bool judge(const V<t3> &xyclist, ll n, ll k, double tm)
{
    if (n == 2) debug_printf("------- tm=%lf\n", tm);
    nnnn = n;

    V<tdd> points;

    for (auto xyc : xyclist) {
        ll x = get<0>(xyc);
        ll y = get<1>(xyc);
        points.pb(tdd((double)x, (double)y));
    }

    rep (idx1, n) srep (idx2, idx1+1, n) {
        double cx1 = get<0>(xyclist[idx1]);
        double cy1 = get<1>(xyclist[idx1]);
        double coef1 = get<2>(xyclist[idx1]);
        double cx2 = get<0>(xyclist[idx2]);
        double cy2 = get<1>(xyclist[idx2]);
        double coef2 = get<2>(xyclist[idx2]);
        double r1 = tm / coef1;
        double r2 = tm / coef2;

        V<tdd> res;
        if (cy1 != cy2) {
            if (solve(res, cx1, cy1, r1, cx2, cy2, r2)) {
                for (auto r : res) points.pb(r);
            }
        }
        else {
            if (solve(res, cy1, cx1, r1, cy2, cx2, r2)) {
                for (auto r : res) points.pb(tdd(get<1>(r), get<0>(r)));
            }
        }
    }

    if (n == 2) {
        debug_printf("---- points\n");
        for (auto p : points) debug_printf("%lf %lf\n", get<0>(p), get<1>(p));
    }

    for (auto p : points) {
        double px = get<0>(p);
        double py = get<1>(p);
        ll cnt = 0;
        for (auto xyc : xyclist) {
            double x = (double)get<0>(xyc);
            double y = (double)get<1>(xyc);
            double coef = (double)get<2>(xyc);
            double r = tm / coef;
            double d = sqrt((px-x)*(px-x) + (py-y)*(py-y));
            if (d <= r + 1e-10) cnt++;
        }
        if (cnt >= k) return true;
    }

    return false;
}

void _main()
{
    ll n; llin(n);
    ll k; llin(k);
    V<t3> xyclist; llinl3(xyclist, n);

    if (k == 1) {
        cout << 0 << endl;
        return;
    }

    double left = 0;
    double right = 1e9;
    double ans = 1e9;

    rep (xx, 100) {
        double now = (left + right) / 2.;
        if (judge(xyclist, n, k, now)) {
            //debug_printf("==== ok\n");
            ans = min(ans, now);
            right = now;
        }
        else {
            // debug_printf("==== ng\n");
            left = now;
        }
    }

    debug_printf("---- ans\n");
    cout << ans << endl;
}

///////////////////////////////////////////////////////////////////////////////


Measured memory_bytes: 3916