#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 {

    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;
            }
        }
    };

    // 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;
    }
}

double getRadian(double x, double y) {
    double radian = atan2(y, x);
    return radian;
}

double getDegree(double radian) {
    if(radian < 0) {
        radian = radian + 2 * M_PI;
    }
    return (radian*360) / (2*M_PI);
}

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

    using namespace Geom;

    int n, k;
    cin >> n >> k;

    vector<Point> point(n);
    vector<double> radius(n);
    vector<pair<double, double> > angle(n);
    REP(i, n) cin >> point[i] >> radius[i];

    REP(i, n) {
        double d = sqrt(point[i].x*point[i].x + point[i].y*point[i].y);
        double center_angle;
        if(point[i].x == 0) {
            if(point[i].y == 0) {
                cout << "1" << endl;
                return 0;
            } else if(point[i].y > 0) {
                center_angle = 90;
            } else {
                center_angle = 270;
            }
        } else {
            center_angle = getDegree(getRadian(point[i].x, point[i].y));
        }

        double center_tangent_angle = getDegree(getRadian(sqrt(d*d - radius[i]*radius[i]), radius[i]));
        angle[i].first = center_angle - center_tangent_angle;
        angle[i].second = center_angle + center_tangent_angle;
        if(0 <= center_angle && center_angle <= 90) {
            if(angle[i].first < 0){
                angle[i].first = 0;
            }
        }
        else if(center_angle <= 180) {
            if(angle[i].second > 180){
                angle[i].second = 180;
            }
        }
        else if(center_angle <= 270.0) {
            if(angle[i].first < 180){
                angle[i].second = 180;
            }
            else{
                angle[i].first = 0, angle[i].second = 0;
            }
        }
        else{
            if(angle[i].second > 360){
                angle[i].first = 0, angle[i].second -=360;
            }
            else{
                angle[i].first = 0, angle[i].second = 0;
            }
        }
        //printf("center = %f\n", center_angle);
        //printf("first = %f, second = %f\n", angle[i].first, angle[i].second);
    }

    REP(i, angle.size()){
        if(angle[i].first == 0 && angle[i].second == 0){
            angle.erase(angle.begin() + i);            
        }
    }

    /* 包含してるものを削除 */
    REP(i, angle.size()) REP(j, angle.size()){
        if(i == j) continue;
        if(angle[j].first <= angle[i].first && angle[i].second <= angle[j].second) {
            angle.erase(angle.begin() + i);
            i--;
            break;
        }
    }

    REP(i, angle.size()){
        //printf("first = %f, second = %f\n", angle[i].first, angle[i].second);
    }

    angle.insert(angle.begin(), {0, 0});
    sort(angle.begin(), angle.end());

    vector<vector<double> > dp;
    dp.assign(n+1, vector<double>(k+1, 0));

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

    print(dp[N][k] / 180);


    return 0;
}



Measured memory_bytes: 20884