Problem: Problem

Great Demon King Megumi wants to defeat the $ N $ hero who lives on the ground.
Megumi can cast explosion magic up to $ M $ times.
Explosion magic is magic that extinguishes heroes who exist within a radius of $ r $ around arbitrary coordinates.
The hero is very thin, so you don't have to consider the size.
All $ M $ explosion spells shall be cast with the same radius.
I decided to use the magic of the minimum radius necessary to annihilate the hero.
Minimize the size of the explosive magic radius.

Constraints

The input satisfies the following conditions.

* $ 1 \ leq M \ leq N \ leq 14 $
* $ 0 \ leq x_i $, $ y_i \ leq 10 ^ 5 $

Input


$ N $ $ M $
$ x_1 $ $ y_1 $
...
$ x_N $ $ y_N $


The input is given in the following format.
The number of heroes $ N $ and the number of explosions to cast $ M $ are given as integers on the first line.
From the second line onward, the coordinates $ x_i $ $, $ $ y_i $ of each hero $ i $ are given as integers.

Output

Output the minimum value of the explosive magic radius as a real number.
Must not contain absolute error greater than $ 10 ^ {-3} $.

Examples

Input

5 2
0 0
5 5
10 10
100 100
200 200


Output

70.710678118755


Input

10 5
321 675
4312 6534
312 532
412 6543
21 43
654 321
543 0
32 5
41 76
5 1


Output

169.824909833728


Input

14 3
312 342
4893 432
321 4
389 4
23 543
0 0
1 1
2 2
432 12
435 32
1 5
2 10
100 100
20 50


Output

218.087711712613


Input

5 2
0 0
0 0
0 0
0 0
0 0


Output

0.000000000001

Solution (in CPP):

Solution:
#include "bits/stdc++.h"
using namespace std;
typedef long long ll;
typedef pair<int, int> pii;
typedef pair<ll, ll> pll;
const int INF = 1e9;
const ll LINF = 1e18;
template<class S,class T> ostream& operator << (ostream& out,const pair<S,T>& o){ out << "(" << o.first << "," << o.second << ")"; return out; }
template<class T> ostream& operator << (ostream& out,const vector<T> V){ for(int i = 0; i < V.size(); i++){ out << V[i]; if(i!=V.size()-1) out << " ";} return out; }
template<class T> ostream& operator << (ostream& out,const vector<vector<T> > Mat){ for(int i = 0; i < Mat.size(); i++) { if(i != 0) out << endl; out << Mat[i];} return out; }
template<class S,class T> ostream& operator << (ostream& out,const map<S,T> mp){ out << "{ "; for(auto it = mp.begin(); it != mp.end(); it++){ out << it->first << ":" << it->second; if(mp.size()-1 != distance(mp.begin(),it)) out << ", "; } out << " }"; return out; }

typedef long double ld;
typedef complex<ld> Point;

const ld eps = 1e-9, pi = acos(-1.0);
namespace std {
    bool operator<(const Point &lhs, const Point &rhs) {
        if (lhs.real() < rhs.real() - eps) return true;
        if (lhs.real() > rhs.real() + eps) return false;
        return lhs.imag() < rhs.imag();
    }
}
Point input_point() { ld x, y; cin >> x >> y; return Point(x, y); } // 点の入力
bool eq(ld a, ld b) { return (abs(a - b) < eps); } // 誤差つき等号判定
ld dot(Point a, Point b) { return real(conj(a) * b); } // 内積
ld cross(Point a, Point b) { return imag(conj(a) * b); } // 外積

// 直線の定義
class Line {
public:
    Point a, b;
    Line() : a(Point(0, 0)), b(Point(0, 0)) {}
    Line(Point a, Point b) : a(a), b(b) {}
    Point operator[](const int _num) {
        if (_num == 0)return a;
        else if (_num == 1)return b;
        else assert(false);
    }
};

// 円の定義
class Circle {
public:
    Point p;
    ld r;
    Circle() : p(Point(0, 0)), r(0) {}
    Circle(Point p, ld r) : p(p), r(r) {}
};

// 垂線の足
Point proj(Line l, Point p) {
    ld t = dot(p - l.a, l.a - l.b) / norm(l.a - l.b);
    return l.a + t * (l.a - l.b);
}

// CCW
int ccw(Point a, Point b, Point c) {
    b -= a; c -= a;
    if (cross(b, c) > eps) return 1;   // a,b,cが反時計周りの順に並ぶ
    if (cross(b, c) < -eps) return -1; // a,b,cが時計周りの順に並ぶ
    if (dot(b, c) < 0) return 2;       // c,a,bの順に直線に並ぶ
    if (norm(b) < norm(c)) return -2;  // a,b,cの順に直線に並ぶ
    return 0;                          // a,c,bの順に直線に並ぶ
}

/* 交差判定 */
// 直線と直線の交差判定
bool isis_ll(Line l, Line m) { return !eq(cross(l.b - l.a, m.b - m.a), 0); }
// 直線と線分の交差判定
bool isis_ls(Line l, Line s) {
    return isis_ll(l, s) &&
    (cross(l.b - l.a, s.a - l.a) * cross(l.b - l.a, s.b - l.a) < eps);
}
// 線分と線分の交差判定
bool isis_ss(Line s, Line t) {
    return ccw(s.a, s.b, t.a) * ccw(s.a, s.b, t.b) <= 0 &&
    ccw(t.a, t.b, s.a) * ccw(t.a, t.b, s.b) <= 0;
}
// 点の直線上判定
bool isis_lp(Line l, Point p) { return (abs(cross(l.b - p, l.a - p)) < eps); }
// 点の線分上判定
bool isis_sp(Line s, Point p) { return (abs(s.a - p) + abs(s.b - p) - abs(s.b - s.a) < eps); }

/* 距離 */
// 直線と直線の交点
Point is_ll(Line s, Line t) {
    Point sv = s.b - s.a, tv = t.b - t.a;
    assert(cross(sv, tv) != 0);
    return s.a + sv * cross(tv, t.a - s.a) / cross(tv, sv);
}

// 直線と点の距離
ld dist_lp(Line l, Point p) {
    return abs(p - proj(l, p));
}

// 直線と直線の距離
ld dist_ll(Line l, Line m) {
    return isis_ll(l, m) ? 0 : dist_lp(l, m.a);
}

// 直線と線分の距離
ld dist_ls(Line l, Line s) {
    return isis_ls(l, s) ? 0 : min(dist_lp(l, s.a), dist_lp(l, s.b));
}

// 線分と点の距離
ld dist_sp(Line s, Point p) {
    Point r = proj(s, p);
    return isis_sp(s, r) ? abs(r - p) : min(abs(s.a - p), abs(s.b - p));
}

// 線分と線分の距離
ld dist_ss(Line s, Line t) {
    if (isis_ss(s, t)) return 0;
    return min({ dist_sp(s, t.a), dist_sp(s, t.b), dist_sp(t, s.a), dist_sp(t, s.b) });
}

/* 円 */
// 円と円の交点
vector<Point> is_cc(Circle c1, Circle c2) {
    vector<Point> res;
    ld d = abs(c1.p - c2.p);
    ld rc = (d * d + c1.r * c1.r - c2.r * c2.r) / (2 * d);
    ld dfr = c1.r * c1.r - rc * rc;
    if (abs(dfr) < eps) dfr = 0.0;
    else if (dfr < 0.0) return res; // no intersection
    ld rs = sqrt(dfr);
    Point diff = (c2.p - c1.p) / d;
    res.push_back(c1.p + diff * Point(rc, rs));
    if (dfr != 0.0) res.push_back(c1.p + diff * Point(rc, -rs));
    return res;
}
// 円と直線の交点
vector<Point> is_lc(Circle c, Line l) {
    vector<Point> res;
    ld d = dist_lp(l, c.p);
    if (d < c.r + eps) {
        ld len = (d > c.r) ? 0.0 : sqrt(c.r * c.r - d * d); //safety;
        Point nor = (l.a - l.b) / abs(l.a - l.b);
        res.push_back(proj(l, c.p) + len * nor);
        res.push_back(proj(l, c.p) - len * nor);
    }
    return res;
}
// 円と線分の距離
vector<Point> is_sc(Circle c, Line l) {
    vector<Point> v = is_lc(c, l), res;
    for (Point p : v)
        if (isis_sp(l, p)) res.push_back(p);
    return res;
}
// 円と点の接線
vector<Line> tangent_cp(Circle c, Point p) {
    vector<Line> ret;
    Point v = c.p - p;
    ld d = abs(v);
    ld l = sqrt(norm(v) - c.r * c.r);
    if (isnan(l)) { return ret; }
    Point v1 = v * Point(l / d, c.r / d);
    Point v2 = v * Point(l / d, -c.r / d);
    ret.push_back(Line(p, p + v1));
    if (l < eps) return ret;
    ret.push_back(Line(p, p + v2));
    return ret;
}
// 円と円の接線
vector<Line> tangent_cc(Circle c1, Circle c2) {
    vector<Line> ret;
    if (abs(c1.p - c2.p) - (c1.r + c2.r) > -eps) {
        Point center = (c1.p * c2.r + c2.p * c1.r) / (c1.r + c2.r);
        ret = tangent_cp(c1, center);
    }
    if (abs(c1.r - c2.r) > eps) {
        Point out = (-c1.p * c2.r + c2.p * c1.r) / (c1.r - c2.r);
        vector<Line> nret = tangent_cp(c1, out);
        ret.insert(ret.end(), nret.begin(), nret.end());
    }
    else {
        Point v = c2.p - c1.p;
        v /= abs(v);
        Point q1 = c1.p + v * Point(0, 1) * c1.r;
        Point q2 = c1.p + v * Point(0, -1) * c1.r;
        ret.push_back(Line(q1, q1 + v));
        ret.push_back(Line(q2, q2 + v));
    }
    return ret;
}

/* 多角形 */
typedef vector<Point> Polygon;
// 面積
ld area(const Polygon &p) {
    ld res = 0;
    int n = (int)p.size();
    for (int j = 0;j < n;j++) res += cross(p[j], p[(j + 1) % n]);
    return res / 2;
}
// 多角形の回転方向
bool is_counter_clockwise(const Polygon &poly) {
    ld angle = 0;
    int n = (int)poly.size();
    for (int i = 0;i < n;i++) {
        Point a = poly[i], b = poly[(i + 1) % n], c = poly[(i + 2) % n];
        angle += arg((c - b) / (b - a));
    }
    return angle > eps;
}
// 凸性判定
bool isConvex(const Polygon &poly){
    int n = (int)poly.size();
    if(n < 3) return false;
    int s = -3;
    for(int i = 0; i < n;i++){
        int r = ccw(poly[(i+n-1)%n],poly[i%n],poly[(i+1)%n]);
        if(r == 1 && s == -3) s = r;
        if(s*r == -1) return false;
    }
    return true;
}
// 円の内外判定
//  2 => out : 0 => on : 1 => in
int is_in_polygon(const Polygon &poly, Point p) {
    ld angle = 0;
    int n = (int)poly.size();
    for (int i = 0;i < n;i++) {
        Point a = poly[i], b = poly[(i + 1) % n];
        if (isis_sp(Line(a, b), p)) return 1;
        angle += arg((b - p) / (a - p));
    }
    return eq(angle, 0) ? 0 : 2;
}
// 凸包 : 凸多角形のある一辺上にある点も含む
Polygon convex_hull(vector<Point> ps) {
    int n = (int)ps.size();
    if (n < 3) return ps;
    sort(ps.begin(), ps.end());
    Polygon u = { ps[0], ps[1] }, l = { ps[n - 1],ps[n - 2] };
    for (int i = 2; i < n; i++) {
        for (int j = (int)u.size(); j >= 2 && ccw(u[j - 2], u[j - 1], ps[i]) >= 0;j--)u.pop_back();
        u.push_back(ps[i]);
    }
    for (int i = n - 3;i >= 0;i--) {
        for (int j = (int)l.size(); j >= 2 && ccw(l[j - 2], l[j - 1], ps[i]) >= 0;j--)l.pop_back();
        l.push_back(ps[i]);
    }
    reverse(l.begin(), l.end());
    for (int i = (int)u.size() - 2; i >= 1; i--)l.push_back(u[i]);
    return l;
}
// 凸包 : 凸多角形のある一辺上にある点を含まない
/*
 Polygon convex_hull(vector<Point> ps) {
 int n = ps.size();
 int k = 0;
 sort(ps.begin(), ps.end());
 Polygon ch(2 * n);
 for (int i = 0; i < n; ch[k++] = ps[i++])
 while (k >= 2 && ccw(ch[k - 2], ch[k - 1], ps[i]) <= 0) --k;
 for (int i = n - 2, t = k + 1; i >= 0; ch[k++] = ps[i--])
 while (k >= t && ccw(ch[k - 2], ch[k - 1], ps[i]) <= 0) --k;
 ch.resize(k - 1);
 return ch;
 }
 */
// 凸多角形の直径
ld convex_diameter(const Polygon& poly){
    int n = (int)poly.size();
    int ii = 0, jj = 0;
    for(int i = 1;i < n;i++){
        if(poly[i].imag() > poly[ii].imag())ii = i;
        if(poly[i].imag() < poly[jj].imag())jj = i;
    }
    ld res = abs(poly[ii] - poly[jj]);
    
    int i, maxi,j,maxj;
    i = maxi = ii; j = maxj = jj;
    do{
        if(cross(poly[(i+1)%n] - poly[i],poly[(j+1)%n] - poly[j]) >= 0) j = (j+1)%n;
        else i = (i+1)%n;
        if(abs(poly[i] - poly[j]) > res){
            res = abs(poly[i] - poly[j]);
            maxi = i; maxj = j;
        }
    }while(i != ii || j != jj);
    return res;
}
// 凸カット
Polygon convex_cut(const Polygon &ps, Line l) {
    int n = (int)ps.size();
    Polygon Q;
    for (int i = 0;i < n;i++) {
        Point A = ps[i], B = ps[(i + 1) % n];
        Line m = Line(A, B);
        if (ccw(l.a, l.b, A) != -1) Q.push_back(A);
        if (ccw(l.a, l.b, A) * ccw(l.a, l.b, B) < 0 && isis_ll(l, m))
            Q.push_back(is_ll(l, m));
    }
    return Q;
}

// 円と多角形の共通部分
double area_of_polygon_and_circle(const Polygon& poly, const Circle c) {
    int n = (int)poly.size();
    ld r = 0;
    for (int i = n - 1, j = 0; j < n; i=j++) {
        Point v = abs(poly[j] - poly[i]) / (poly[j] - poly[i]);
        if (poly[j] == poly[i])continue;
        assert(poly[j] != poly[i]);
        Point a = (poly[i] - c.p)*v, b = (poly[j] - c.p)*v;
        ld d = norm(c.r) - norm(a.imag());
        if (abs(a.imag()) < eps) continue;
        if (d < 0)d = 0;
        d = sqrt(d);
        double l, m;
        r += norm(c.r)*((l = atan2(b.imag(), min(b.real(), -d)) - atan2(a.imag(), min(a.real(), -d)))
                        + (m = atan2(b.imag(), max(b.real(), d)) - atan2(a.imag(), max(a.real(), d))))
        + a.imag()*(min(d, max(a.real(), -d)) - max(-d, min(b.real(), d)));
        assert(-pi < l && -pi < m && l < pi && m < pi);
    }
    return r / 2;
}

/*
 <url:>
 問題文============================================================
 
 =================================================================
 
 解説=============================================================
 
 ================================================================
 */
typedef Point P;
template <class iter>
std::pair<P, ld> min_ball(iter left, iter right, int seed = 1333) {
    const int n = right - left;
    
    assert(n >= 1);
    if (n == 1) {
        return {*left, ld(0)};
    }
    
    std::mt19937 mt(seed);
    std::shuffle(left, right, mt);
    // std::random_shuffle(left, right); // simple but deprecated
    
    iter ps = left;
    using circle = std::pair<P, ld>;
    
    auto make_circle_3 = [](const P &a, const P &b, const P &c) -> circle {
        ld A = std::norm(b - c), B = std::norm(c - a), C = std::norm(a - b),
        S = cross(b - a, c - a);
        P p = (A * (B + C - A) * a + B * (C + A - B) * b + C * (A + B - C) * c) / (4 * S * S);
        ld r2 = std::norm(p - a);
        return {p, r2};
    };
    
    auto make_circle_2 = [](const P &a, const P &b) -> circle {
        P c = (a + b) / (ld)2;
        ld r2 = std::norm(a - c);
        return {c, r2};
    };
    
    auto in_circle = [](const P &a, const circle &c) -> bool {
        return std::norm(a - c.first) <= c.second + eps;
    };
    
    circle c = make_circle_2(ps[0], ps[1]);
    
    // MiniDisc
    for (int i = 2; i < n; ++i) {
        if (!in_circle(ps[i], c)) {
            // MiniDiscWithPoint
            c = make_circle_2(ps[0], ps[i]);
            for (int j = 1; j < i; ++j) {
                if (!in_circle(ps[j], c)) {
                    // MiniDiscWith2Points
                    c = make_circle_2(ps[i], ps[j]);
                    for (int k = 0; k < j; ++k) {
                        if (!in_circle(ps[k], c)) {
                            c = make_circle_3(ps[i], ps[j], ps[k]);
                        }
                    }
                }
            }
        }
    }
    return c;
}

#define MAX_N 15
#define MAX_M 15
ll N,M;
Point p[MAX_N];

// dp[S][cnt] := 死んでいる勇者がSでcnt回爆発を行なっている時の最小半径
ld dp[1<<MAX_N][MAX_M];


vector<pair<ld,ll>> St;
void init(){
    for(int i = 0;i < (1<<MAX_N);i++)for(int j = 0;j < MAX_M;j++) dp[i][j] = -1;
}

ld rec(ll S,ll cnt,int p){
    ld& res = dp[S][cnt];
    if(S==((1<<N)-1)) return 0;
    if(cnt==M) return LINF;
    if(!(res < 0)) return res;
    res = LINF;
    for(int i = p; i < St.size();i++){
        if(S == (S|St[i].second)) continue;
        res = min(res,max(St[i].first,rec(S|St[i].second,cnt+1,i+1)));
    }
    return res;
}



int main(void) {
    cin.tie(0); ios::sync_with_stdio(false);
    init();
    cin >> N >> M;
    for(int i = 0; i < N;i++) p[i] = input_point();
    
    // 最小包含円
    for(int i = 1; i < (1<<N);i++){
        vector<P> tp;
        for(int j = 0; j < N;j++){
            if((i>>j)&1){
                tp.push_back(p[j]);
            }
        }
        auto c = min_ball(tp.begin(),tp.end());
//        cout << bitset<10>(i) << " " << c << endl;
        St.push_back({sqrt(c.second),i});
    }
    
    cout << fixed << setprecision(12) << rec(0,0,0) << endl;
    return 0;
}