Problem: Some of you know an old story of Voronoi Island. There were N liege lords and they are always involved in territorial disputes. The residents of the island were despaired of the disputes.

One day, a clever lord proposed to stop the disputes and divide the island fairly. His idea was to divide the island such that any piece of area belongs to the load of the nearest castle. The method is called Voronoi Division today.

Actually, there are many aspects of whether the method is fair. According to one historian, the clever lord suggested the method because he could gain broader area than other lords.

Your task is to write a program to calculate the size of the area each lord can gain. You may assume that Voronoi Island has a convex shape.



Input

The input consists of multiple datasets. Each dataset has the following format:

N M
Ix1 Iy1
Ix2 Iy2
...
IxN IyN
Cx1 Cy1
Cx2 Cy2
...
CxM CyM


N is the number of the vertices of Voronoi Island; M is the number of the liege lords; (Ixi, Iyi) denotes the coordinate of the i-th vertex; (Cxi, Cyi ) denotes the coordinate of the castle of the i-the lord.

The input meets the following constraints: 3 ≤ N ≤ 10, 2 ≤ M ≤ 10, -100 ≤ Ixi, Iyi, Cxi, Cyi ≤ 100. The vertices are given counterclockwise. All the coordinates are integers.

The last dataset is followed by a line containing two zeros. This line is not a part of any dataset and should not be processed.

Output

For each dataset, print the area gained by each liege lord with an absolute error of at most 10-4 . You may output any number of digits after the decimal point. The order of the output areas must match that of the lords in the input.

Example

Input

3 3
0 0
8 0
0 8
2 2
4 2
2 4
0 0


Output

9.0
11.5
11.5

Solution (in CPP):

Solution:
#include<bits/stdc++.h>
#define EPS (1e-10)
#define equals(a,b) (fabs((a)-(b)) < EPS)
 
using namespace std;

static const int COUNTER_CLOCKWISE = 1;
static const int CLOCKWISE = -1;
static const int ONLINE_BACK = 2;
static const int ONLINE_FRONT = -2;
static const int ON_SEGMENT = 0;

struct Point{
  double x,y;
  Point(){}
  Point(double x,double y) :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 k) {return Point(x*k,y*k);}
  Point operator / (double k) {return Point(x/k,y/k);}
  double norm(){return x*x+y*y;}
  double abs(){return sqrt(norm());}

  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;
typedef vector<Point> Polygon;

struct Segment{
  Point p1,p2;
  Segment(){}
  Segment(Point p1, Point p2):p1(p1),p2(p2){}
};
typedef Segment Line;

struct Circle{
  Point c;
  double r;
  Circle(Point c,double r):c(c),r(r){}
};

double norm(Vector a){
  return a.x*a.x+a.y*a.y;
}
double abs(Vector a){
  return sqrt(norm(a));
}
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 isOrthogonal(Vector a,Vector b){
  return equals(dot(a,b),0.0);
}

bool isOrthogonal(Point a1,Point a2,Point b1,Point b2){
  return isOrthogonal(a1-a2,b1-b2);
}

bool isOrthogonal(Segment s1,Segment s2){
  return equals(dot(s1.p2-s1.p1,s2.p2-s2.p1),0.0);
}

bool isParallel(Vector a,Vector b){
  return equals(cross(a,b),0.0);
}

bool isParallel(Point a1,Point a2,Point b1,Point b2){
  return isParallel(a1-a2,b1-b2);
}

bool isParallel(Segment s1,Segment s2){
  return equals(cross(s1.p2-s1.p1,s2.p2-s2.p1),0.0); 
}

Point project(Segment s,Point p){
  Vector base=s.p2-s.p1;
  double r=dot(p-s.p1,base)/norm(base);
  return s.p1+base*r;
}

Point reflect(Segment s,Point p){
  return p+(project(s,p)-p)*2.0;
}

int ccw(Point p0,Point p1,Point p2){
  Vector a = p1-p0;
  Vector b = p2-p0;
  if(cross(a,b) > EPS) return COUNTER_CLOCKWISE;
  if(cross(a,b) < -EPS) return CLOCKWISE;
  if(dot(a,b) < -EPS) return ONLINE_BACK;
  if(a.norm()<b.norm()) return ONLINE_FRONT;
  return ON_SEGMENT;
}

bool intersect(Point p1,Point p2,Point p3,Point p4){
  return (ccw(p1,p2,p3)*ccw(p1,p2,p4) <= 0 &&
	  ccw(p3,p4,p1)*ccw(p3,p4,p2) <= 0 );
}

bool intersect(Segment s1,Segment s2){
  return intersect(s1.p1,s1.p2,s2.p1,s2.p2);
}

double getDistanceLP(Line l,Point p){
  return abs(cross(l.p2-l.p1,p-l.p1)/abs(l.p2-l.p1));
}

double getDistanceSP(Segment s,Point p){
  if(dot(s.p2-s.p1,p-s.p1) < 0.0 ) return abs(p-s.p1);
  if(dot(s.p1-s.p2,p-s.p2) < 0.0 ) return abs(p-s.p2);
  return getDistanceLP(s,p);
}

double getDistance(Segment s1,Segment s2){
  if(intersect(s1,s2)) return 0.0;
  return min(min(getDistanceSP(s1,s2.p1),getDistanceSP(s1,s2.p2)),
	     min(getDistanceSP(s2,s1.p1),getDistanceSP(s2,s1.p2)));
}

Point getCrossPoint(Segment s1,Segment s2){
  Vector base=s2.p2-s2.p1;
  double d1=abs(cross(base,s1.p1-s2.p1));
  double d2=abs(cross(base,s1.p2-s2.p1));
  double t=d1/(d1+d2);
  return s1.p1+(s1.p2-s1.p1)*t;
}


pair<Point,Point> getCrossPoints(Circle c,Line l){
  Vector pr=project(l,c.c);
  Vector e=(l.p2-l.p1)/abs(l.p2-l.p1);
  double base=sqrt(c.r*c.r-norm(pr-c.c));
  return make_pair(pr+e*base,pr-e*base);
}


double arg(Vector p){
  return atan2(p.y,p.x);
}

Vector polar(double a,double r){
  return Point(cos(r)*a,sin(r)*a);
}

pair<Point,Point> getCrossPoints(Circle c1,Circle c2){
  double d=abs(c1.c-c2.c);
  double a=acos((c1.r*c1.r+d*d-c2.r*c2.r)/(2*c1.r*d));
  double t=arg(c2.c-c1.c);
  return make_pair(c1.c+polar(c1.r,t+a),c1.c+polar(c1.r,t-a));
}

int contains(Polygon g,Point p){
  int n=g.size();
  bool x=false;
  for(int i=0;i<n;i++){
    Point a=g[i]-p,b=g[(i+1)%n]-p;
    if(fabs(cross(a,b)) < EPS && dot(a,b) < EPS) return 1;
    if(a.y>b.y) swap(a,b);
    if(a.y < EPS && EPS < b.y && cross(a,b) > EPS ) x = !x;
  }
  return (x?2:0);
}

Polygon andrewScan(Polygon s){
  Polygon u,l;
  if(s.size()<3) return s;
  sort(s.begin(),s.end());
  u.push_back(s[0]);
  u.push_back(s[1]);
  l.push_back(s[s.size()-1]);
  l.push_back(s[s.size()-2]);
  for(int i=2;i<(int)s.size();i++){
    for(int n=u.size();n>=2&&ccw(u[n-2],u[n-1],s[i]) != CLOCKWISE;n--){
      u.pop_back();
    }
    u.push_back(s[i]);
  } 
  for(int i=s.size()-3;i>=0;i--){
    for(int n=l.size();n>=2&&ccw(l[n-2],l[n-1],s[i]) != CLOCKWISE;n--){
      l.pop_back();
    }
    l.push_back(s[i]);
  }
  reverse(l.begin(),l.end());
  for(int i=u.size()-2;i>=1;i--) l.push_back(u[i]);
  return l;
} 

double area(Polygon s){
  double res=0;
  for(int i=0;i<(int)s.size();i++){
    res+=cross(s[i],s[(i+1)%s.size()])/2.0;
  }
  return abs(res);
}

Point getCrossPointLL(Line l1,Line l2){
  double a=cross(l1.p2-l1.p1,l2.p2-l2.p1);
  double b=cross(l1.p2-l1.p1,l1.p2-l2.p1);
  if(abs(a)<EPS&&abs(b)<EPS) return l2.p1;
  return l2.p1+(l2.p2-l2.p1)*(b/a);
}

Polygon convexCut(Polygon p,Line l){
  Polygon q;
  for(int i=0;i<(int)p.size();i++){
    Point a=p[i],b=p[(i+1)%p.size()];
    if(ccw(l.p1,l.p2,a)!=-1) q.push_back(a);
    if(ccw(l.p1,l.p2,a)*ccw(l.p1,l.p2,b)<0)
      q.push_back(getCrossPointLL(Line(a,b),l));
  }
  return q;
}

Line bisector(Point p1,Point p2){
  Circle c1=Circle(p1,abs(p1-p2)),c2=Circle(p2,abs(p1-p2));
  pair<Point,Point> p=getCrossPoints(c1,c2);
  if(cross(p2-p1,p.first-p1)>0) swap(p.first,p.second);
  return Line(p.first,p.second);
}

int main(){
  int n,m;
  while(cin>>n>>m,n||m){
    Polygon p,q;
    for(int i=0;i<n;i++){
      double x,y;
      cin>>x>>y;
      p.push_back(Point(x,y));
    }
    for(int i=0;i<m;i++){
      double x,y;
      cin>>x>>y;
      q.push_back(Point(x,y));
    }
    for(int i=0;i<m;i++){
      Polygon t=p;
      //cout<<area(t)<<" ";
      for(int j=0;j<m;j++){
	if(i==j) continue;
	t=convexCut(t,bisector(q[i],q[j]));
      }
      printf("%.10lf\n",area(t));
    }
  }
  return 0;
}