#include <bits/stdc++.h>

using namespace std;

#define int long long
#define FOR(i, a, b) for(ll i = (a); i < (b); ++i)
#define FORR(i, a, b) for(ll i = (a); i > (b); --i)
#define REP(i, n) for(ll i = 0; i < (n); ++i)
#define REPR(i, n) for(ll i = n; i >= 0; i--)
#define FOREACH(x, a) for(auto &(x) : (a))
#define VECCIN(x)                                                              \
    for(auto &youso_ : (x)) cin >> youso_
#define bitcnt __builtin_popcount
#define SZ(x) ((ll)(x).size())
#define fi first
#define se second
#define All(a) (a).begin(), (a).end()
template <typename T = long long> inline T IN() {
    T x;
    cin >> x;
    return (x);
}
inline void CIN() {}
template <class Head, class... Tail>
inline void CIN(Head &&head, Tail &&... tail) {
    cin >> head;
    CIN(move(tail)...);
}
#define CCIN(...)                                                              \
    char __VA_ARGS__;                                                          \
    CIN(__VA_ARGS__)
#define DCIN(...)                                                              \
    double __VA_ARGS__;                                                        \
    CIN(__VA_ARGS__)
#define LCIN(...)                                                              \
    ll __VA_ARGS__;                                                            \
    CIN(__VA_ARGS__)
#define SCIN(...)                                                              \
    string __VA_ARGS__;                                                        \
    CIN(__VA_ARGS__)
#define Printv(v)                                                              \
    {                                                                          \
        REP(x, v.size()) { cout << v[x] << (x == v.size() - 1 ? "\n" : " "); } \
    }
template <typename T = string> inline void eputs(T s) {
    cout << s << "\n";
    exit(0);
}
template <typename A, size_t N, typename T>
void Fill(A (&array)[N], const T &val) {
    std::fill((T *)array, (T *)(array + N), val);
}
template <typename T> using PQG = priority_queue<T, vector<T>, greater<T>>;
template <typename T> using PQ = priority_queue<T>;

typedef long long ll;
typedef vector<ll> VL;
typedef vector<VL> VVL;
typedef pair<ll, ll> PL;

const int INF = 1e9;
const int MOD = 1e9 + 7;
const double PI = atan(1.0) * 4.0;
// const int MOD = 998244353;
const ll LINF = 1e18;
const ll dx[] = {1, 0, -1, 0};
const ll dy[] = {0, 1, 0, -1};

void cinfast() {
    cin.tie(0);
    ios::sync_with_stdio(false);
}

/* 基本要素 */
using D = double;     // 座標値の型。doubleかlong doubleを想定
using P = complex<D>; // Point
using L = pair<P, P>; // Line
using VP = vector<P>;
const D EPS = 1e-9; // 許容誤差。問題によって変える;

#define X real()
#define Y imag()
#define LE(n, m) ((n) < (m) + EPS)
#define GE(n, m) ((n) + EPS > (m))
#define EQ(n, m) (abs((n) - (m)) < EPS)

using PDD = pair<double, double>;
double dp[1501][1501];

signed main() {
    LCIN(N, K);
    vector<PDD> ang;
    REP(i, N) {
        DCIN(x, y, r);
        double d = sqrt(x * x + y * y);
        double q = atan2(y, x);
        if(q < -PI / 2) q += PI * 2;
        double v = asin((double)r / d);
        ang.emplace_back(
            make_pair(max(0.0, min(PI, q - v)), min(PI, max(0.0, q + v))));
    }
    sort(All(ang));
    ll sz = 0;
    vector<PDD> com;
    REP(i, N) {
        bool id = true;
        REP(j, N) {
            if(i != j && ang[j].fi < ang[i].fi && ang[i].se < ang[j].se)
                id = false;
        }
        if(id) {
            com.emplace_back(ang[i]);
            sz++;
        }
    }
    double ans = 0;
    REP(i, K) {
        double tmp = 0;
        ll pre = 0;
        REP(j, sz) {
            while(com[pre].se < com[j].fi) {
                tmp = max(tmp, dp[i][pre]);
                pre++;
            }
            dp[i + 1][j] = max(tmp + com[j].se - com[j].fi,
                               dp[i][pre] + com[j].se - com[pre].se);
            ans = max(ans, dp[i + 1][j]);
        }
    }
    printf("%.9f\n", ans / PI);
}


Measured memory_bytes: 21312