/**

 旋转卡壳，，

 **/

 #include <iostream>

 #include <algorithm>

 #include <cmath>

 #include <cstdio>

 using namespace std;

 const double eps = 1e-;

 struct point {

     double x,y;

     point(double x=,double y =):x(x),y(y){}

 };

 int dcmp(double x){

     if(fabs(x)<eps)

         return ;

     else

         return x<?-:;

 }

 point p[],p1[];

 point q[],q1[];

 int maxid,minid;

 int N,M;

 typedef point Vector;

 Vector operator -(point a,point b){

     return Vector(a.x-b.x,a.y-b.y);

 }

 double cross(Vector a,Vector b){

     return a.x*b.y-a.y*b.x;

 }

 double dot(Vector a,Vector b){

     return a.x*b.x+a.y*b.y;

 }

 bool  cmp(point a,point b){

     if(a.x==b.x)

         return a.y<b.y;

     return a.x<b.x;

 }

 bool operator ==(const point &a,const point &b){

     return dcmp(a.x-b.x)==&&dcmp(a.y-b.y)==;

 }

 double length(Vector a){

     return sqrt(a.x*a.x+a.y*a.y);

 }

 int convexHull(point *p,int n,point *ch){

     sort(p,p+n,cmp);

     int m =;

     for(int i=;i<n;i++){

         while(m>&&cross(ch[m-]-ch[m-],p[i]-ch[m-])<=)

             m--;

         ch[m++] = p[i];

     }

     int k =m;

     for(int i = n-;i>=;i--){

         while(m>k&&cross(ch[m-]-ch[m-],p[i]-ch[m-])<=)

             m--;

         ch[m++] = p[i];

     }

     if(n>) m--;

     return m;

 }

 double distanceToSegment(point p,point a,point b){

     if(a==b)

         return length(p-a);

     Vector v1 = b-a,v2 = p-a, v3 = p-b;

     if(dcmp(dot(v1,v2))<)

         return length(v2);

     else if(dcmp(dot(v1,v3))>)

         return length(v3);

     else

         return fabs(cross(v1,v2))/length(v1);

 }

 double distanceBetweenSegment(point a,point b,point c,point d){

     return min(min(distanceToSegment(a,c,d),distanceToSegment(b,c,d)),min(distanceToSegment(c,a,b),distanceToSegment(d,a,b)));

 }

 void getMaxAndMin(int &maxid,int &minid){

     maxid =;

     minid =;

     for(int i=;i<N;i++){

         if(p1[i].y<p1[minid].y)

             minid =i;

     }

     for(int i=;i<M;i++){

         if(q1[i].y>q1[maxid].y)

             maxid = i;

     }

 }

 double solve(point *p,point *q,int minid,int maxid,int N,int M){

     double temp,ret = 1e5;

     p[N] = p[];

     q[M] = q[];

     for(int i=;i<N;i++){

         while(temp = dcmp(cross(q[maxid]-q[maxid+],p[minid+]-p[minid]))>){

             maxid = (maxid+)%M;

         }

         if(temp<)

             ret = min(ret,distanceToSegment(q[maxid],p[minid],p[minid+]));

         else

             ret = min(ret,distanceBetweenSegment(p[minid],p[minid+],q[maxid],q[maxid+]));

         minid = (minid+)%N;

     }

     return ret;

 }

 int main()

 {

     while(cin>>N>>M){

         if(N==&&M==)

             break;

         for(int i=;i<N;i++)

             cin>>p[i].x>>p[i].y;

         for(int i=;i<M;i++)

             cin>>q[i].x>>q[i].y;

         N = convexHull(p,N,p1);

         M = convexHull(q,M,q1);

         getMaxAndMin(maxid,minid);

         double ans = solve(p1,q1,minid,maxid,N,M);

         printf("%.5lf\n",ans);

     }

     return ;

 }