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 <iostream>
#include <vector>
#include <cmath>
#include <iomanip>
using namespace std;

template<class T> inline bool chmax(T& a, T b) { if (a < b) { a = b; return 1; } return 0; }
template<class T> inline bool chmin(T& a, T b) { if (a > b) { a = b; return 1; } return 0; }

/* 幾何ライブラリ */
using DD = double;
const DD INF = 1LL<<60;      // to be set appropriately
const DD EPS = 1e-10;        // to be set appropriately
const DD PI = acosl(-1.0);
DD torad(int deg) {return (DD)(deg) * PI / 180;}
DD todeg(DD ang) {return ang * 180 / PI;}

/* Point */
struct Point {
    DD x, y;
    Point(DD x = 0.0, DD y = 0.0) : x(x), y(y) {}
    friend ostream& operator << (ostream &s, const Point &p) {return s << '(' << p.x << ", " << p.y << ')';}
};
inline Point operator + (const Point &p, const Point &q) {return Point(p.x + q.x, p.y + q.y);}
inline Point operator - (const Point &p, const Point &q) {return Point(p.x - q.x, p.y - q.y);}
inline Point operator * (const Point &p, DD a) {return Point(p.x * a, p.y * a);}
inline Point operator * (DD a, const Point &p) {return Point(a * p.x, a * p.y);}
inline Point operator * (const Point &p, const Point &q) {return Point(p.x * q.x - p.y * q.y, p.x * q.y + p.y * q.x);}
inline Point operator / (const Point &p, DD a) {return Point(p.x / a, p.y / a);}
inline Point conj(const Point &p) {return Point(p.x, -p.y);}
inline Point rot(const Point &p, DD ang) {return Point(cos(ang) * p.x - sin(ang) * p.y, sin(ang) * p.x + cos(ang) * p.y);}
inline Point rot90(const Point &p) {return Point(-p.y, p.x);}
inline DD cross(const Point &p, const Point &q) {return p.x * q.y - p.y * q.x;}
inline DD dot(const Point &p, const Point &q) {return p.x * q.x + p.y * q.y;}
inline DD norm(const Point &p) {return dot(p, p);}
inline DD abs(const Point &p) {return sqrt(dot(p, p));}
inline DD amp(const Point &p) {DD res = atan2(p.y, p.x); if (res < 0) res += PI*2; return res;}
inline bool eq(const Point &p, const Point &q) {return abs(p - q) < EPS;}
inline bool operator < (const Point &p, const Point &q) {return (abs(p.x - q.x) > EPS ? p.x < q.x : p.y < q.y);}
inline bool operator > (const Point &p, const Point &q) {return (abs(p.x - q.x) > EPS ? p.x > q.x : p.y > q.y);}
inline Point operator / (const Point &p, const Point &q) {return p * conj(q) / norm(q);}

/* Line */
struct Line : vector<Point> {
    Line(Point a = Point(0.0, 0.0), Point b = Point(0.0, 0.0)) {
        this->push_back(a);
        this->push_back(b);
    }
    friend ostream& operator << (ostream &s, const Line &l) {return s << '{' << l[0] << ", " << l[1] << '}';}
};

// 1：a-bから見てcは左側(反時計回り)、-1：a-bから見てcは右側(時計回り)、0：一直線上
int simple_ccw(const Point &a, const Point &b, const Point &c) {
    if (cross(b-a, c-a) > EPS) return 1;
    if (cross(b-a, c-a) < -EPS) return -1;
    return 0;
}

// 円や直線の交点
vector<Point> crosspoint(const Line &l, const Line &m) {
    vector<Point> res;
    DD d = cross(m[1] - m[0], l[1] - l[0]);
    if (abs(d) < EPS) return vector<Point>();
    res.push_back(l[0] + (l[1] - l[0]) * cross(m[1] - m[0], m[1] - l[0]) / d);
    return res;
}

// 外心
Point gaisin(Point a, Point b, Point c) {
    Line ab((a+b)/2, (a+b)/2 + rot90(a-b));
    Line bc((b+c)/2, (b+c)/2 + rot90(b-c));
    return crosspoint(ab, bc)[0];
}

// 最小包含円
DD mic(const vector<Point> &v) {
    int N = (int)v.size();
    if (N <= 1) return 0;

    // 候補
    vector<Point> alt;
    for (int i = 0; i < N; ++i) {
        for (int j = i+1; j < N; ++j) {
            alt.push_back( (v[i] + v[j]) / 2 );
            for (int k = j+1; k < N; ++k) {
                if (simple_ccw(v[i], v[j], v[k]) == 0) continue;
                auto r = gaisin(v[i], v[j], v[k]);
                alt.push_back(r);
            }
        }
    }

    // 調べる
    DD res = INF;
    for (auto r : alt) {
        DD tmp = 0;
        for (auto p : v) chmax(tmp, abs(p - r));
        chmin(res, tmp);
    }
    return res;
}


int main() {
    int N, M; cin >> N >> M;
    vector<Point> v(N);
    for (int i = 0; i < N; ++i) cin >> v[i].x >> v[i].y;

    // pre
    vector<DD> need(1<<N, 0);
    for (int bit = 0; bit < (1<<N); ++bit) {
        vector<Point> part;
        for (int i = 0; i < N; ++i) {
            if (bit & (1<<i)) part.push_back(v[i]);
        }
        need[bit] = mic(part);

        //cout << bit << ": " << need[bit] << endl;
    }
        
    // bitDP
    vector<vector<DD>> dp(M+1, vector<DD>(1<<N,INF));
    dp[0][0] = 0;
    for (int m = 0; m < M; ++m) {
        for (int bit = 0; bit < (1<<N); ++bit) {
            int rem = ((1<<N)-1) - bit;
            for (int bit2 = rem; ; bit2 = (bit2-1) & rem) {
                chmin(dp[m+1][bit|bit2], max(dp[m][bit], need[bit2]));
                if (!bit2) break;
            }
        }
    }
    
    cout << fixed << setprecision(10) << dp[M][(1<<N)-1] << endl;
}