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<cstdio>
#include<algorithm>
#include<iostream>
#include<cmath>
#include<vector>
#include<cstdlib>
#include<cassert>
#include<map>
#include<iomanip>
#define _A_ true
#define EPS 1e-10
#define COUNTER_CLOCKWISE 1
#define CLOCKWISE -1 
#define ONLINE_BACK 2
#define ONLINE_FRONT -2
#define ON_SEGMENT 0
using namespace std;
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);} //もし悪を使うなら要確認
 
  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 Point;
struct Segment{
public:
  Point p1,p2;
  Segment(Point p = Point(),Point pp = Point()):p1(p),p2(pp){}
};
 
typedef vector<Point> Polygon;
typedef Segment Line;

class Voronoi
{
public:
  Polygon poly;
 
  Voronoi(Polygon poly):poly(poly){}

  double norm(Point p){
    return p.x*p.x+p.y*p.y;
  }
 
  double abs(Point p){
    return sqrt(norm(p));
  }
 
  Point polar(double a,double rad){
    return Point(a*cos(rad),a*sin(rad));
  }
 
  double args(Point p){
    return atan2(p.y,p.x);
  }
 
  double dot(Point a,Point b){
    return a.x*b.x+a.y*b.y;
  }
 
  double cross(Point a,Point b){
    return a.x*b.y-b.x*a.y;
  }
 
  Point project(Segment s,Point p){
    Point base = s.p2 - s.p1;
    double t = dot(p-s.p1,base)/base.norm();
    return s.p1+base*t;
  }
 
  Point reflect (Segment s, Point p){
    return p + (project(s,p)-p)*2.0;
  }
 
  int ccw(Point p0,Point p1,Point p2){
    Point a = p1-p0;
    Point 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 isIntersect(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 isIntersect(Segment s1,Segment s2){
    return isIntersect(s1.p1,s1.p2,s2.p1,s2.p2);
  }

  Point getCrossPointSegments(Segment s1,Segment s2){
    //assert(isIntersect(s1,s2));
    Point 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;
  }


  Point getCrossPointLines( Line s1, Line s2){

    Point a = s1.p2 - s1.p1;
    Point base = s2.p2 -s2.p1;
    return s1.p1 + a * (cross(base, s2.p1 - s1.p1)/cross(base, a));
  }

  Polygon cutPolygon( Polygon P, Line l ){
    Polygon u;
    
    for ( int i = 0; i < P.size(); i++ ){
      Point a = P[i], b = P[(i+1)%P.size()];
	
      if ( ccw(l.p1, l.p2, a) != CLOCKWISE ) u.push_back(a);
      if ( ccw(l.p1, l.p2, a) * ccw(l.p1, l.p2, b) == -1 ){
	u.push_back(getCrossPointLines(Segment(a, b), l));
      }
    }   
    return u;
  } 
 
  Line CreateLine(Point p,Point pp){
    Point mid = (p+pp)/2;
    Point sl = pp-p;//原点に5
    double rad = args(sl);
    Point ap = polar(abs(sl),rad+M_PI/2)+mid;
    //ap.x = abs(sl)*cos(rad+M_PI/2)+mid.x;
    //ap.y = abs(sl)*sin(rad+M_PI/2)+mid.y;
    return Line(mid,ap);
  } 
 
  double AreaCalc(Polygon p){
    double area = 0;
    for(int i=0;i<p.size();i++)
      area+=cross(p[i],p[(i+1)%p.size()]);
    return fabs(area)/2.0;
  } 

  //サイトposに対するボロノイセルV(pos)の面積を返す 
  //pointsは多角形の中に存在するサイトの集合]
  //posはpoints中の自分の位置
  double getAreaOfVoronoi(vector<Point>& points,int pos)
  {
    Polygon polx = poly;
    int N = points.size();
    for(int i=0;i<N;i++)
      if(i != pos)
	polx = cutPolygon(polx,CreateLine(points[pos],points[i]));
    return AreaCalc(polx);
  }  

};

int main(){

  int N,M;
  while(cin >> N >> M,N|M){
  
  vector<Point> l(N);
  vector<Point> C(M);
  for(int i=0;i<N;i++)
    {
      cin >> l[i].x >> l[i].y;
      l[i].x += 200,l[i].y += 200;
    }
  for(int i=0;i<M;i++)
    {
      cin >> C[i].x >> C[i].y;
      C[i].x += 200,C[i].y += 200;
    }
  for(int i=0;i<M;i++)
    {

      Polygon poly; 
      for(int j=0;j<N;j++)
	poly.push_back(l[j]);
      Voronoi vor(poly);

      cout << setiosflags(ios::fixed) << setprecision(4) << vor.getAreaOfVoronoi(C,i) << endl;

    }  

  }
  return 0;
}