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>
#define FOR(i, a, n) for(ll i = (ll)a; i < (ll)n; i++)
#define rep(i, n) FOR(i, 0, n)
#define ALL(x) (x).begin(), (x).end()
using namespace std;
typedef long long ll;

constexpr ll mod = 1e9 + 7;

template <typename T> inline bool chmax(T &a, const T b) {
    if(a >= b) return false;
    a = b;
    return true;
}
template <typename T> inline bool chmin(T &a, const T b) {
    if(a <= b) return false;
    a = b;
    return true;
}

/*-------------------------------------------*/

using Real = long double;
using Point = complex<Real>;
const Real EPS = 1e-12, PI = acos(-1.0L);

inline bool eq(Real a, Real b) { return fabs(b - a) < EPS; }

istream &operator>>(istream &is, Point &p) {
    Real a, b;
    is >> a >> b;
    p = Point(a, b);
    return is;
}

struct Circle {
    Point p;
    Real r;

    Circle() = default;

    Circle(Point p, Real r) : p(p), r(r) {}
};

using Points = vector<Point>;
using Circles = vector<Circle>;

bool intersect(Circle c1, Circle c2) {
    if(c1.r < c2.r) swap(c1, c2);
    Real d = abs(c1.p - c2.p);
    if(c1.r + c2.r < d || c1.r - c2.r > d) return false;
    return true;
}

pair<Point, Point> crossPoint(const Circle &c1, const Circle &c2) {
    Real d = abs(c1.p - c2.p);
    Real a = acos((c1.r * c1.r + d * d - c2.r * c2.r) / (2 * c1.r * d));
    Real t = atan2(c2.p.imag() - c1.p.imag(), c2.p.real() - c1.p.real());
    Point p1 = c1.p + Point(cos(t + a) * c1.r, sin(t + a) * c1.r);
    Point p2 = c1.p + Point(cos(t - a) * c1.r, sin(t - a) * c1.r);
    return make_pair(p1, p2);
}

int N, K;
Points P;
vector<int> c;
Circles C;

bool isOk(long double mid) {
    rep(i, N) C[i] = Circle(P[i], mid / c[i]);
    Points Check;
    rep(i, N) {
        Check.push_back(P[i]);
        rep(j, i) if(intersect(C[i], C[j])) {
            pair<Point, Point> tmp = crossPoint(C[i], C[j]);
            Check.push_back(tmp.first);
            Check.push_back(tmp.second);
        }
    }
    for(Point p : Check) {
        int cnt = 0;
        rep(i, N) if(abs(P[i] - p) <= C[i].r + EPS) cnt++;
        if(cnt >= K) return true;
    }
    return false;
}

int main() {
    cin.tie(0);
    ios::sync_with_stdio(0);

    cin >> N >> K;
    P.resize(N);
    c.resize(N);
    C.resize(N);
    rep(i, N) cin >> P[i] >> c[i];

    long double ok = 1e6, ng = 0;
    while(ok - ng > 1e-6) {
        long double mid = (ng + ok) / 2;
        (isOk(mid) ? ok : ng) = mid;
    }
    cout << fixed << setprecision(20) << ok << endl;
}