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>
                                        #include<iostream>
                                        #include<cstdio>
                                        #include<vector>
                                        #include<queue>
                                        #include<map>
                                        #include<cstring>
                                        #include<string>
                                        #include <math.h>
                                        #include<algorithm>
                                    //    #include <boost/multiprecision/cpp_int.hpp>
                                        #include<functional>
                               #define int long long
                                        #define inf  1000000007
                                        #define pa pair<int,int>
                                        #define ll long long
                                        #define pal pair<double,double>
                                        #define ppap pair<pa,int>
                                  
                                        #define ssa pair<string,int>
                                        #define  mp make_pair
                                        #define  pb push_back
                                        #define EPS (1e-8)
                                        #define equals(a,b) (fabs((a)-(b))<EPS)
int dx[4]={0,-1,0,1};
int dy[4]={1,0,-1,0};
                                        using namespace std;
                               			class pa3{
                                        	public:
                                        	int x,y,z;
                                        	pa3(int x=0,int y=0,int z=0):x(x),y(y),z(z) {}
                                        	bool operator < (const pa3 &p) const{
                                        		if(x!=p.x) return x<p.x;
                                        		if(y!=p.y) return y<p.y;
                                        		 return z<p.z;
                                        		//return x != p.x ? x<p.x: y<p.y;
                                        	}
                               				bool operator > (const pa3 &p) const{
                                        		if(x!=p.x) return x>p.x;
                                        		if(y!=p.y) return y>p.y;
                                        		 return z>p.z;
                                        		//return x != p.x ? x<p.x: y<p.y;
                                        	}
                                        	bool operator == (const pa3 &p) const{
                                        		return x==p.x && y==p.y && z==p.z;
                                        	}
                                        		bool operator != (const pa3 &p) const{
                                        			return !( x==p.x && y==p.y && z==p.z);
                                        	}
                                        
                                        };
                                        
                                        class pa4{
                                        	public:
                                        	double x;
                                        	int y,z,w;
                                        	pa4(double x=0,int y=0,int z=0,int w=0):x(x),y(y),z(z),w(w) {}
                                        	bool operator < (const pa4 &p) const{
                                        		if(x!=p.x) return x<p.x;
                                        		if(y!=p.y) return y<p.y;
                                        		if(z!=p.z)return z<p.z;
                                        		return w<p.w;
                                        		//return x != p.x ? x<p.x: y<p.y;
                                        	}
                                        	bool operator > (const pa4 &p) const{
                                        		if(x!=p.x) return x>p.x;
                                        		if(y!=p.y) return y>p.y;
                                        		if(z!=p.z)return z>p.z;
                                        		return w>p.w;
                                        		//return x != p.x ? x<p.x: y<p.y;
                                        	}
                                        	bool operator == (const pa4 &p) const{
                                        		return x==p.x && y==p.y && z==p.z &&w==p.w;
                                        	}
                                        		
                                        
                                        };
                                        class pa2{
                                        	public:
                                        	int x,y;
                                        	pa2(int x=0,int y=0):x(x),y(y) {}
                                        	pa2 operator + (pa2 p) {return pa2(x+p.x,y+p.y);}
                                        	pa2 operator - (pa2 p) {return pa2(x-p.x,y-p.y);}
                                        	pa2 operator * (int a) {return pa2(x*a,y*a);}
                                        	bool operator < (const pa2 &p) const{
                                        		return x != p.x ? x<p.x: y<p.y;
                                        	}
                                        	bool operator > (const pa2 &p) const{
                                        		return x != p.x ? x>p.x: y>p.y;
                                        	}
                                        	bool operator == (const pa2 &p) const{
                                        		return abs(x-p.x)==0 && abs(y-p.y)==0;
                                        	}
                                        	bool operator != (const pa2 &p) const{
                                        		return !(abs(x-p.x)==0 && abs(y-p.y)==0);
                                        	}
                                        		
                                        
                                        };
                                        
                                               #define ppa pair<int,pas>
                                        class Point{
                                        	public:
                                        	double x,y;
                                        	Point(double x=0,double y=0):x(x),y(y) {}
                                        	Point operator + (Point p) {return Point(x+p.x,y+p.y);}
                                        	Point operator - (Point p) {return Point(x-p.x,y-p.y);}
                                        	Point operator * (double a) {return Point(x*a,y*a);}
                                        	Point operator / (double a) {return Point(x/a,y/a);}
                                        	double absv() {return sqrt(norm());}
                                        	double norm() {return x*x+y*y;}
                                        	bool operator < (const Point &p) const{
                                        		return x != p.x ? x<p.x: y<p.y;
                                        	}
                                        	bool operator == (const Point &p) const{
                                        		return fabs(x-p.x)<EPS && fabs(y-p.y)<EPS;
                                        	}
                                        };
                                        typedef Point Vector;
                                 #define pl pair<int,pas>
                                        struct Segment{
                                        Point p1,p2;
                                        };
                                         double dot(Vector a,Vector b){
                                        	return a.x*b.x+a.y*b.y;
                                        }
                                        double cross(Vector a,Vector b){
                                        	return a.x*b.y-a.y*b.x;
                                        }
                                    
            bool parareru(Point a,Point b,Point c,Point d){
            //	if(abs(cross(a-b,d-c))<EPS)cout<<"dd "<<cross(a-b,d-c)<<endl;
            	return abs(cross(a-b,d-c))<EPS;
            }
            double distance_ls_p(Point a, Point b, Point c) {
              if ( dot(b-a, c-a) < EPS ) return (c-a).absv();
              if ( dot(a-b, c-b) < EPS ) return (c-b).absv();
              return abs(cross(b-a, c-a)) / (b-a).absv();
            }
            bool is_intersected_ls(Segment a,Segment b) {
            	if(a.p1==b.p1||a.p2==b.p1||a.p1==b.p2||a.p2==b.p2) return false;
            	if(parareru((a.p2),(a.p1),(a.p1),(b.p2))&&parareru((a.p2),(a.p1),(a.p1),(b.p1))){
            //		cout<<"sss"<<endl;
            		if(dot(a.p1-b.p1,a.p1-b.p2)<EPS) return true;
            		if(dot(a.p2-b.p1,a.p2-b.p2)<EPS) return true;
            		if(dot(a.p1-b.p1,a.p2-b.p1)<EPS) return true;
            		if(dot(a.p1-b.p2,a.p2-b.p2)<EPS) return true;
            		return false;
            	}
              else return ( cross(a.p2-a.p1, b.p1-a.p1) * cross(a.p2-a.p1, b.p2-a.p1) < EPS ) && ( cross(b.p2-b.p1, a.p1-b.p1) * cross(b.p2-b.p1, a.p2-b.p1) < EPS );
            }
             
            double segment_dis(Segment a,Segment b){
            	if(is_intersected_ls(a,b))return 0;
            	double r=distance_ls_p(a.p1, a.p2, b.p1);
            	r=min(r,distance_ls_p(a.p1, a.p2, b.p2));
            	r=min(r,distance_ls_p(b.p1, b.p2, a.p2));
            	r=min(r,distance_ls_p(b.p1, b.p2, a.p1));
            	return r;
            }
            Point intersection_ls(Segment a, Segment b) {
              Point ba = b.p2-b.p1;
              double d1 = abs(cross(ba, a.p1-b.p1));
              double d2 = abs(cross(ba, a.p2-b.p1));
              double t = d1 / (d1 + d2);
             
              return a.p1 + (a.p2-a.p1) * t;
            }
             
                            string itos( int i ) {
                            ostringstream s ;
                            s << i ;
                            return s.str() ;
                            }
                             
                            int gcd(int v,int b){
                            	if(v>b) return gcd(b,v);
                            	if(v==b) return b;
                            	if(b%v==0) return v;
                            	return gcd(v,b%v);
                            }
             
                            double distans(double x1,double y1,double x2,double y2){
                            	double rr=(x1-x2)*(x1-x2)+(y1-y2)*(y1-y2);
                            	return sqrt(rr);
                            	
                            }
             /*               
            int pr[1000010];
            int inv[1000010];
            
            int beki(int wa,int rr,int warukazu){
            	if(rr==0) return 1%warukazu;
            	if(rr==1) return wa%warukazu;
            	if(rr%2==1) return (beki(wa,rr-1,warukazu)*wa)%warukazu;
            	int zx=beki(wa,rr/2,warukazu);
            	return (zx*zx)%warukazu;
            }
double bekid(double w,int r){
	if(r==0) return 1.0;
	if(r==1) return w;
	if(r%2) return bekid(w,r-1)*w;
	double f=bekid(w,r/2);
	return f*f;
}

            
			int comb(int nn,int rr){
				int r=pr[nn]*inv[rr];
				r%=inf;
				r*=inv[nn-rr];
				r%=inf;
				return r;
			}
            
            
            void gya(int ert){
            	pr[0]=1;
            	for(int i=1;i<=ert;i++){
            		pr[i]=(pr[i-1]*i)%inf;
            	}
           	for(int i=0;i<=ert;i++) inv[i]=beki(pr[i],inf-2,inf);
            	
            }
            */ 
			//priority_queue<pa3,vector<pa3>,greater<pa3>> pq;            
             //sort(ve.begin(),ve.end(),greater<int>());
                                     //----------------kokomade tenpure------------
            //vector<double> ans(100000000),ans2(100000000)
/*
struct Segmin{
	//       1
	//   2        3
	// 4   5   6    7
	
	
	private:
	public:
	
	// (1<<15)=32768
	// 1<<16 = 65536
	// 1<<17 = 131072
	// 1<<18 = 262144
	
	int cor=(1<<17);
	
	vector<pa> vec;
	
	void shoki1(){
		
		vec.resize(2*cor+3, mp(0,0));
		for(int i=cor;i<2*cor;i++)vec[i].second=1;
	}
		void shoki2(){
			for(int i=cor-1;i>0;i--) {
				if(vec[2*i].first<vec[2*i+1].first) vec[i]=vec[2*i];
				else if(vec[2*i].first>vec[2*i+1].first)vec[i]=vec[2*i+1];
				else vec[i]=mp(vec[2*i].first,vec[2*i].second+vec[2*i+1].second);
			}
		}
		
	void updadd(int x,int w){
		//x ���ڂ� w���Z
		x+=cor;
		vec[x].first+=w;
		while(1){
			x/=2;
			if(x==0) break;
			if(vec[2*x].first<vec[2*x+1].first) vec[x]=vec[2*x];
			else if(vec[2*x].first>vec[2*x+1].first) vec[x]=vec[2*x+1];
			else vec[x]=mp(vec[2*x].first,vec[2*x].second+vec[2*x+1].second);
		}
		
	}
	
	void updchan(int x,int w){
		//x���ڂ�w�ɕύX
		x+=cor;
		vec[x].first=w;
		while(1){
			x/=2;
			if(x==0) break;
			if(vec[2*x].first<vec[2*x+1].first) vec[x]=vec[2*x];
			else if(vec[2*x].first>vec[2*x+1].first) vec[x]=vec[2*x+1];
			else vec[x]=mp(vec[2*x].first,vec[2*x].second+vec[2*x+1].second);
		}
		
	}
	// [a,b)
	// k-th node
	// k no kukanha [l,r)
	pa segmin(int a,int b,int k=1,int l=0,int r=-10){
		if(r<0)r=cor;
		
	//	cout<<a<<" "<<b<<" "<<k<<" "<<l<<" "<<r<<endl;
		
		if(a<=l && r<=b){
			return vec[k];
		}
		if(r<=a || b<=l){
			return mp((1ll<<31)-1,-1);
		}
		
		pa v1=segmin(a,b,k*2,l,(l+r)/2),v2=segmin(a,b,k*2+1,(l+r)/2,r);
		
		if(v1.first<v2.first)return v1;
		else if(v1.first>v2.first) return v2;
		else return mp(v1.first,v1.second+v2.second);
	}
	
};



struct Segmax{
	//       1
	//   2        3
	// 4   5   6    7
	
	
	private:
	public:
	
	// (1<<15)=32768
	// 1<<16 = 65536
	// 1<<17 = 131072
	// 1<<18 = 262144
	
	int cor=(1<<17);
	
	vector<pa> vec;
	
	void shoki1(){
		
		vec.resize(2*cor+3, mp(0,0));
		for(int i=cor;i<2*cor;i++)vec[i].second=1;
	}
		void shoki2(){
			for(int i=cor-1;i>0;i--) {
				if(vec[2*i].first>vec[2*i+1].first) vec[i]=vec[2*i];
				else if(vec[2*i].first<vec[2*i+1].first)vec[i]=vec[2*i+1];
				else vec[i]=mp(vec[2*i].first,vec[2*i].second+vec[2*i+1].second);
			}
		}
		
	void updadd(int x,int w){
		//x ���ڂ� w���Z
		x+=cor;
		vec[x].first+=w;
		while(1){
			x/=2;
			if(x==0) break;
			if(vec[2*x].first>=vec[2*x+1].first) vec[x]=vec[2*x];
			else vec[x]=vec[2*x+1];
		}
		
	}
	
	void updchan(int x,int w){
		//x���ڂ�w�ɕύX
		x+=cor;
		vec[x].first=w;
		while(1){
			x/=2;
			if(x==0) break;
			if(vec[2*x].first>vec[2*x+1].first) vec[x]=vec[2*x];
			else if(vec[2*x].first<vec[2*x+1].first) vec[x]=vec[2*x+1];
			else vec[x]=mp(vec[2*x].first,vec[2*x].second+vec[2*x+1].second);
		}
		
	}
	// [a,b)
	// k-th node
	// k no kukanha [l,r)
	pa segmax(int a,int b,int k=1,int l=0,int r=-10){
		if(r<0)r=cor;
		
	//	cout<<a<<" "<<b<<" "<<k<<" "<<l<<" "<<r<<endl;
		
		if(a<=l && r<=b){
			return vec[k];
		}
		if(r<=a || b<=l){
			return mp(-(1ll<<31),-1);
		}
		
		pa v1=segmax(a,b,k*2,l,(l+r)/2),v2=segmax(a,b,k*2+1,(l+r)/2,r);
		
		if(v1.first>v2.first)return v1;
		else if(v1.first<v2.first) return v2;
		else return mp(v1.first,v1.second+v2.second);
	}
	
};
*/
set<pa> se;
Point p[30];
double dp[1<<14][15];
bool sumi[1<<14]={0};
double rd[1<<14];
int n;

bool icc(int i,int j,int k){
	return abs(cross(p[i]-p[j],p[i]-p[k]))<EPS; 
}

Point kai(Point v){
	return (Point){-v.y,v.x};
}

double solve(int r){
	
	if(sumi[r] )return rd[r];
	int d= __builtin_popcount(r);
	if(d==1) {
		sumi[r]=1;
		rd[r]=0;
		return 0;
	}
		vector<int> ve;
	if(d==2){
	
		for(int i=0;i<n;i++)if(r&(1<<i)) ve.pb(i);
		rd[r]=(p[ve[0]]-p[ve[1]]).absv()/2.0;
		sumi[r]=1;
		return rd[r];
	}
	
	for(int i=0;i<n;i++)if(r&(1<<i)) ve.pb(i);
	double ans=1000000000;
	for(int i=0;i<d;i++)for(int j=i+1;j<d;j++){
		Point c=(p[ve[i]]+p[ve[j]])/2.0;
		double rr=(c-p[ve[i]]).absv();
		
		for(int k=0;k<d;k++)if((p[ve[k]]-c).absv()>rr+EPS) goto lll;
		
		//if(r==7) cout<<"d"<<endl;
		ans=min(ans,rr);
		
		lll:;
	}
	
	for(int i=0;i<d;i++)for(int j=i+1;j<d;j++)for(int k=j+1;k<d;k++){
		if(icc(ve[i],ve[j],ve[k])) continue;
		
		Point x1,x2,v1,v2;
		x1=(p[ve[i]]+p[ve[j]])/2.0;
		x2=(p[ve[i]]+p[ve[k]])/2.0;
		v1=kai(p[ve[i]]-p[ve[j]]);
		v2=kai(p[ve[i]]-p[ve[k]]);
	
		double det=1.0/(v2.x*v1.y-v1.x*v2.y);
		double t,s;
		t=-v2.y*(x2.x-x1.x)+v2.x*(x2.y-x1.y);
		s=-v1.y*(x2.x-x1.x)+v1.x*(x2.y-x1.y);
		t*=det;
		s*=det;
		Point c=x1+v1*t;
		double rr=(c-p[ve[i]]).absv();
		for(int kk=0;kk<d;kk++)if((p[ve[kk]]-c).absv()>rr+EPS) goto lll2;
		ans=min(ans,rr);
		
		lll2:;
		
	}
	
	rd[r]=ans;
	sumi[r]=1;
//	cout<<bitset<10>(r)<<" "<<ans<<endl;
	return ans;
}


signed main(){
	
int m;
	for(int i=0;i<(1<<14);i++)for(int j=0;j<15;j++)dp[i][j]=1000000000.0;
	
	cin>>n>>m;
	for(int i=0;i<n;i++){
		int y,yy;
		cin>>y>>yy;
		se.insert(mp(y,yy));
	}
	
	int cn=0;
	for(auto it=se.begin();it!=se.end();it++){
		p[cn].x=(*it).first;
		p[cn].y=(*it).second;
		cn++;
		
	}
	
	n=cn;
	
	if(n<=m){
	cout<<0<<endl;
		return 0;
	}
	if(n==2){
		printf("%.10lf\n",((p[0]-p[1]).absv())/2.0);
		return 0;
	
	}
	dp[0][0]=0.0;
	
	for(int i=1;i<(1<<n);i++)for(int j=1;j<=m;j++){
		
		for(int jj=i;jj>0;jj=(jj-1)&i){
			dp[i][j]=min(dp[i][j],max(dp[i^jj][j-1],solve(jj)));
			//cout<<solve(j)<<endl;
		}
	//	cout<<bitset<5>(i)<<" "<<j<<" "<<dp[i][j]<<endl;
	}
	printf("%.10lf\n",dp[-1+(1<<n)][m]);
	
	return 0;
	
        }