// aribon3-6_f
#include <bits/stdc++.h>
#ifdef LOCAL
#include "../cxx-prettyprint/prettyprint.hpp"
#endif
using namespace std;

typedef long long ll;
typedef unsigned long long ull;
typedef pair<int, int> P;

#define REP(i, n) for (int (i) = 0 ; (i) < (int)(n) ; ++(i))
#define REPN(i, m, n) for (int (i) = m ; (i) < (int)(n) ; ++(i))
#define REP_REV(i, n) for (int (i) = (int)(n) - 1 ; (i) >= 0 ; --(i))
#define REPN_REV(i, m, n) for (int (i) = (int)(n) - 1 ; (i) >= m ; --(i))
#define ALL(x) x.begin(), x.end()

#define INF ((1 << 29)-1)
#define MOD (1000000007)

#define print2D(h, w, arr) REP(i, h) { REP(j, w) cout << arr[i][j] << " "; cout << endl; }
template<class T> void print(const T& x){cout << x << endl;}
template<class T, class... A> void print(const T& first, const A&... rest) { cout << first << " "; print(rest...); }
struct PreMain {PreMain(){cin.tie(0);ios::sync_with_stdio(false);cout<<fixed<<setprecision(20);}} premain;

// ベクトル
namespace Geom {
    #define _USE_MATH_DEFINES

    const double eps = 1e-9;

    struct Point {
        double x, y;
        explicit Point(double x=0, double y=0): x(x), y(y) {}
        Point& operator+=(const Point& v){ x += v.x; y+= v.y; return *this;}
        Point operator+(const Point& v) const{return Point(*this) += v;}
        Point& operator-=(const Point& v){x -= v.x; y-= v.y; return *this;}
        Point operator-(const Point& v) const{return Point(*this) -= v;}
        Point& operator*=(double s){x *= s; y *= s; return *this;}
        Point operator*(double s) const{return Point(*this) *= s;}
        Point& operator/=(double s){x /= s; y /= s; return *this;}
        Point operator/(double s) const{return Point(*this) /= s;}
        double dot(const Point& v) const {return x*v.x + y*v.y;}        /* 内積 */
        double cross(const Point& v) const {return x*v.y - v.x*y;}      /* 外積 */
        double norm2() const {return x*x + y*y;}                        /* ノルムの二乗*/
        double norm() const {return sqrt(norm2());}                     /* ノルム */
        int quadrant() const { if(y > 0) return x>0 ? 1:2; else return x>0 ? 4:3;} /* 象限判定 */
        Point rot(double theta) {return Point(cos(theta) * x - sin(theta) * y, sin(theta) * x + cos(theta) * y);} // 回転
        Point rot90() {return Point(-y, x);} // 90度回転
    };
    ostream& operator<<(ostream& os, const Point& v) {os<<"("<<v.x<<","<<v.y<<")"; return os;}
    istream& operator>>(istream& is, Point& v){ is >> v.x >> v.y; return is;}

    // 点a, b, cからなる三角形の面積
    double calc_triangle_area(Point a, Point b, Point c) {
        Point v1 = b - a;
        Point v2 = c - a;
        return abs(v1.cross(v2)) / 2;
    }

    // 点a, bを通る直線と点cとの距離
    double calc_distance_between_point_and_line(Point a, Point b, Point c) {
        return abs((b-a).cross(c-a)) / (b-a).norm();
    }

    // 点a, bを端点とする線分と点cとの距離
    double calc_distance_between_point_and_segment(Point a, Point b, Point c) {
        if ((b-a).dot(c-a) < eps) return (c-a).norm();
        if ((a-b).dot(c-b) < eps) return (c-b).norm();
        return calc_distance_between_point_and_line(a, b, c);
    }

    // 点a, bを端点とする線分と点cと点dを端点とする線分の距離
    double calc_distance_between_segments(Point a, Point b, Point c, Point d) {
        double d0 = calc_distance_between_point_and_segment(a, b, c);
        double d1 = calc_distance_between_point_and_segment(a, b, d);
        double d2 = calc_distance_between_point_and_segment(c, d, a);
        double d3 = calc_distance_between_point_and_segment(c, d, b);
        return min(min(d0, d1), min(d2, d3));
    }

    enum RELATION_BETWEEN_SEGMENT_AND_POINT {
        COUNTER_CLOCKWISE = 1,     // p1とp2のp0を挟んだ位置関係が反時計回り
        CLOCKWISE = -1,            // 時計回り
        ONLINE_BACK = 2,           // p1とp2がp0を挟んで直線状にある
        ONLINE_FRONT = -2,         // p0とp2の間にp1がある
        ON_SEGMENT = 0,            // p0とp1の間にp2がある
    };

    // 点cが点a, bを端点とする線分のどちら側にあるか、enumで返す
    RELATION_BETWEEN_SEGMENT_AND_POINT ccw_ex(Point p0, Point p1, Point p2) {
        Point v1 = p1 - p0;
        Point v2 = p2 - p0;
        if(v1.cross(v2) > eps) return COUNTER_CLOCKWISE;    // 1
        if(v1.cross(v2) < -eps) return CLOCKWISE;           // -1
        if(v1.dot(v2) < -eps) return ONLINE_BACK;           // 2
        if(v1.norm() < v2.norm()) return ONLINE_FRONT;      // -2
        return ON_SEGMENT;                                  // 0
    }

    // 点cが点a, bを端点とする線分のどちら側にあるか
    int ccw(Point p0, Point p1, Point p2) {
        Point v1 = p1 - p0;
        Point v2 = p2 - p0;
        if(v1.cross(v2) > eps) return 1;
        if(v1.cross(v2) < -eps) return -1;
        return 0;
    }

    // p1,p2を端点とする線分Aとp3,p4を端点とする線分Bの交差判定
    // include_end=trueなら端点が重なっていても交差しているとみなす
    bool intersect(Point p1, Point p2, Point p3, Point p4, bool include_end=true) {

        bool is_otherside;
        bool is_inside;

        if (include_end){
            is_otherside = ccw(p1,p2,p3) * ccw(p1,p2,p4) <= 0; // Aの両側にBの端点があるかどうか。どちらかがAの直線状にいてもOK
            is_inside = ccw(p3,p4,p1) * ccw(p3,p4,p2) <= 0;    // Aの端点の内側にBがいるかどうか。
        } else {
            is_otherside = ccw(p1,p2,p3) * ccw(p1,p2,p4) < 0; // Aの両側にBの端点があるかどうか
            is_inside = ccw(p3,p4,p1) * ccw(p3,p4,p2) < 0;    // Aの端点の内側にBがいるかどうか
        }
        return is_otherside && is_inside;
    }


    // 円
    struct Circle {
        Point c;
        double r;
        Circle(){}
        Circle(Point c, double r):c(c),r(r){}

        // 円が点pを含むかどうか　include_circumは円周上を含むとするかどうか
        bool does_include_point(Point p, bool include_circum = true){
            double d = (p - c).norm();
            if (include_circum){
                return d < r + eps;
            } else {
                return d < r - eps;
            }
        }
    };
    ostream& operator<<(ostream& os, const Circle& c) {os<<"("<<c.c<<","<<c.r<<")"; return os;}
    istream& operator>>(istream& is, Circle& c){ is >> c.c >> c.r; return is;}

    // 点p1, p2を通る半径rの円を返す
    vector<Circle> calc_circle_on_two_points(Point p1, Point p2, double r){

        Point p12_half = (p2 - p1) / 2.0;

        double n_vec_norm2 = r*r - p12_half.norm2();
        if (n_vec_norm2 < 0) return vector<Circle>();

        double n_vec_norm = sqrt(n_vec_norm2);
        Point n_vec = p12_half.rot90() * n_vec_norm / p12_half.norm();

        vector<Circle> ret;
        ret.emplace_back(p1 + p12_half + n_vec, 1.0);
        ret.emplace_back(p1 + p12_half - n_vec, 1.0);
        return ret;
    }

    // 点pを通る、円Cの２つの接線の傾きの角度を返す [0, 2π]で返す
    pair<double, double> calc_tangent_line_on_circle(Circle c, Point p){
        Point pc = c.c - p;
        double angle0 = atan2(pc.y, pc.x);
        double l2 = pc.norm2() - c.r*c.r;
        if (l2 < 0) {
            return {0, 2*M_PI};
        }
        double l = sqrt(l2);
        double angle1 = angle0 - atan2(c.r, l);
        double angle2 = angle0 + atan2(c.r, l);
        angle1 = angle1 >= 0 ? angle1 : angle1 + 2*M_PI;
        angle2 = angle2 >= 0 ? angle2 : angle2 + 2*M_PI;

        return {angle1, angle2};
    }

}


int main() {
#ifdef LOCAL
    ifstream in("../arg.txt"); cin.rdbuf(in.rdbuf());
#endif

    using namespace Geom;

    int N, K;
    cin >> N >> K;
    vector<Circle> circles(N);
    REP(i, N) cin >> circles[i];

    vector<pair<double, double>> intervals(N);
    REP(i, N){
        auto thetas = calc_tangent_line_on_circle(circles[i], Point(0.0, 0.0));
        if (thetas.first == 0 && thetas.second == 2*M_PI) {
            print(1.0);
            return 0;
        }

        if (thetas.first >= M_PI && thetas.second >= M_PI){
            intervals[i] = {0, 0};
        } else if (thetas.first >= M_PI) {
            intervals[i] = {0, thetas.second};
        } else if (thetas.second >= M_PI){
            intervals[i] = {thetas.first, M_PI};
        } else {
            intervals[i] = {thetas.first, thetas.second};
        }
    }

    // 他の要素に包含される要素を削除
    REP(i, intervals.size()) REP(j, intervals.size()){
        if (i == j) continue;

        if (intervals[j].first <= intervals[i].first && intervals[i].second <= intervals[j].second) {
            intervals.erase(intervals.begin() + i);
            i--;
            break;
        }
    }

    intervals.insert(intervals.begin(), {0, 0});
    sort(ALL(intervals));

    vector<vector<double>> dp;
    dp.assign(N+1, vector<double>(K+1, 0));

    int n = intervals.size()-1;
    REPN(i, 1, n+1){
        //
        int l = i;
        while (l > 0){
            l--;
            if (intervals[l].second < intervals[i].first){
                break;
            }
        }
        REPN(j, 1, K+1){
            dp[i][j] = dp[i-1][j];
            dp[i][j] = max(dp[i][j], dp[l][j-1] + intervals[i].second - intervals[i].first);
            dp[i][j] = max(dp[i][j], dp[l+1][j-1] + intervals[i].second - intervals[l+1].second);
        }
    }

    print(dp[n][K] / M_PI);

    return 0;
}



Measured memory_bytes: 20988