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 range(i,a,b) for(int i = (a); i < (b); i++)
#define rep(i,b) for(int i = 0; i < (b); i++)
#define all(a) (a).begin(), (a).end()
#define show(x)  cerr << #x << " = " << (x) << endl;
using namespace std;

template<typename T>
ostream& operator << (ostream& os, vector<T>& v){
	rep(i,v.size()){ os << v[i] << (i == v.size() - 1 ? "" : " "); } return os;
}
template<typename T>
istream& operator >> (istream& is, vector<T>& v){
	for(T& x: v){ is >> x; } return is;
}

typedef complex<double> Point;
typedef Point Vector;
struct Segment{					//線分を表す構造体
	Point p1, p2;
	Segment(Point p1 = Point(), Point p2 = Point()) : p1(p1), p2(p2) {}
};
typedef Segment Line;			//直線を表す構造体
typedef vector<Point> Polygon;	//多角形を表す構造体

namespace std{
	bool operator < (const Point &a, const Point &b){
		return real(a) != real(b) ? real(a) < real(b) : imag(a) < imag(b);
	}
	bool operator == (const Point &a, const Point &b){
		return a.real() == b.real() && a.imag() == b.imag();
	}
}

class Circle{
	public:
		Point p;
		double r;
		Circle(Point p = Point(), double r = 0.0): p(p), r(r) {}
};

// 許容する誤差
#define EPS (1e-10)
#define INF (1e10)

// ベクトルaの絶対値を求める
//double length = abs(a);

// 2点a,b間の距離を求める
//double distance = abs(a-b);

/*
// ベクトルaの単位ベクトルを求める
Point b = a / abs(a);

// ベクトルaの法線ベクトルn1,n2を求める
Point n1 = a * Point(0, 1);
Point n2 = a * Point(0, -1);
*/

int ccw(Point, Point, Point);

// 2つのスカラーが等しいかどうか
bool EQ(double a, double b){
	return (abs(a - b) < EPS);
}

// 2つのベクトルが等しいかどうか
bool EQV(Vector a, Vector b){
	return ( EQ(a.real(), b.real()) && EQ(a.imag(), b.imag()) );
}

// 内積 (dot product) : a・b = |a||b|cosΘ
double dot(Point a, Point b) {
	return (a.real() * b.real() + a.imag() * b.imag());
}

// 外積 (cross product) : a×b = |a||b|sinΘ
double cross(Point a, Point b) {
	return (a.real() * b.imag() - a.imag() * b.real());
}

// 2直線の直交判定 : a⊥b <=> dot(a, b) = 0
bool isOrthogonal(Point a1, Point a2, Point b1, Point b2) {
	return EQ( dot(a1-a2, b1-b2), 0.0 );
}
bool isOrthogonal(Line s1, Line s2) { return isOrthogonal(s1.p1, s1.p2, s2.p1, s2.p2); }

// 2直線の平行判定 : a//b <=> cross(a, b) = 0
bool isParallel(Point a1, Point a2, Point b1, Point b2) {
	return EQ( cross(a1-a2, b1-b2), 0.0 );
}
bool isParallel(Line s1, Line s2) { return isParallel(s1.p1, s1.p2, s2.p1, s2.p2); }

// 点cが直線a,b上にあるかないか
bool isPointOnLine(Point a, Point b, Point c) {
	return EQ( cross(b-a, c-a), 0.0 );
}
bool isPointOnLine(Line s, Point c) { return isPointOnLine(s.p1, s.p2, c); }

// 点a,bを通る直線と点cとの距離
double distanceLPoint(Point a, Point b, Point c) {
	return abs(cross(b-a, c-a)) / abs(b-a);
}
double distanceLPoint(Line s, Point c) { return distanceLPoint(s.p1, s.p2, c); }

// 点a,bを端点とする線分と点cとの距離
double distanceLsPoint(Point a, Point b, Point c) {
	if ( dot(b-a, c-a) < EPS ) return abs(c-a);
	if ( dot(a-b, c-b) < EPS ) return abs(c-b);
	return abs(cross(b-a, c-a)) / abs(b-a);
}
double distanceLsPoint(Segment s, Point c) { return distanceLsPoint(s.p1, s.p2, c); }

// a1,a2を端点とする線分とb1,b2を端点とする線分の交差判定
// 端点が重なる場合も、線分が交差しているとみなす
bool isIntersectedLs(Point a1, Point a2, Point b1, Point b2) {
	return ( ccw(a1, a2, b1) * ccw(a1, a2, b2) <= 0 &&
			ccw(b1, b2, a1) * ccw(b1, b2, a2) <= 0 );
}
bool isIntersectedLs(Segment s1, Segment s2) { return isIntersectedLs(s1.p1, s1.p2, s2.p1, s2.p2); }

// 端点が重なっているかを検出する
bool isContainSamePoints(Segment s1, Segment s2){
	if(abs(s1.p1 - s2.p1) < EPS) return true;
	if(abs(s1.p1 - s2.p2) < EPS) return true;
	if(abs(s1.p2 - s2.p1) < EPS) return true;
	if(abs(s1.p2 - s2.p2) < EPS) return true;
	return false;
}

// a1,a2を端点とする線分とb1,b2を端点とする線分の交点計算
Point intersectionLs(Point a1, Point a2, Point b1, Point b2) {
	Vector base = b2 - b1;
	double d1 = abs(cross(base, a1 - b1));
	double d2 = abs(cross(base, a2 - b1));
	double t = d1 / (d1 + d2);

	return Point(a1 + (a2 - a1) * t);
}
Point intersectionLs(Segment s1, Segment s2) { return intersectionLs(s1.p1, s1.p2, s2.p1, s2.p2); }

// a1,a2を通る直線とb1,b2を通る直線の交差判定
bool isIntersectedL(Point a1, Point a2, Point b1, Point b2) {
	return !EQ( cross(a1-a2, b1-b2), 0.0 );
}
bool isIntersectedL(Line l1, Line l2) { return isIntersectedL(l1.p1, l1.p2, l2.p1, l2.p2); }

// a1,a2を通る直線とb1,b2を通る直線の交点計算
Point intersectionL(Point a1, Point a2, Point b1, Point b2) {
	Point a = a2 - a1; Point b = b2 - b1;
	return a1 + a * cross(b, b1-a1) / cross(b, a);
}
Point intersectionL(Line l1, Line l2) { return intersectionL(l1.p1, l1.p2, l2.p1, l2.p2); }

// 線分s1と線分s2の距離
double distanceLL(Segment s1, Segment s2){
	if(isIntersectedLs(s1.p1, s1.p2, s2.p1, s2.p2) ) return 0.0;
	return min(
			min(distanceLsPoint(s1.p1, s1.p2, s2.p1),
				distanceLsPoint(s1.p1, s1.p2, s2.p2)),
			min(distanceLsPoint(s2.p1, s2.p2, s1.p1),
				distanceLsPoint(s2.p1, s2.p2, s1.p2)) );
}
double distanceLL(Point p0, Point p1, Point p2, Point p3){
	Segment s1 = Segment{p0, p1}, s2 = Segment{p2, p3};
	return distanceLL(s1, s2);
}

// 線分sに対する点pの射影
Point project(Segment s, Point p){
	Vector base = s.p2 - s.p1;
	double r = dot(p - s.p1, base) / norm(base);
	return Point(s.p1 + base * r);
}

//線分sを対象軸とした点pの線対称の点
Point reflect(Segment s, Point p){
	return Point(p + (project(s, p) - p) * 2.0);
}

//点pをangle分だけ時計回りに回転
Point rotation(Point p, double angle){
	double x, y;
	x = p.real() * cos(angle) - p.imag() * sin(angle);
	y = p.real() * sin(angle) + p.imag() * cos(angle);
	return Point(x, y);
}

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

//円c1と円c2の交点
double arg(Vector p) { return atan2(p.imag(), p.real()); }
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.p - c2.p);
	double a = acos((c1.r * c1.r + d * d - c2.r * c2.r) / (2 * c1.r * d));
	double t = arg(c2.p - c1.p);
	return make_pair(Point(c1.p + polar(c1.r, t + a)), Point(c1.p + polar(c1.r, t - a)));
}

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;

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( abs(a) < abs(b) ) return ONLINE_FRONT;

	return ON_SEGMENT;
}

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

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

Line bisector(Point a, Point b) {
	Point A = (a + b) * Point(0.5, 0);
	return Line(A, A + (b - a) * Point(0, M_PI / 2));
}

Polygon voronoiCell(Polygon g, vector<Point> v, int s) {
	rep(i, v.size()){
		if (i != s) g = convexCut(g, bisector(v[s], v[i]));
	}
	return g;
}

//三角形の面積
double areaOfTriangle(Point a, Point b, Point c){
	double w, x, y, z;
	w = b.real()-a.real();
	x = b.imag()-a.imag();
	y = c.real()-a.real();
	z = c.imag()-a.imag();
	return abs((w * z - x * y) / 2);
}

//多角形の面積
double areaOfPolygon(Polygon g){
	int n = g.size();
	double ret = 0.0;
	rep(i,n) ret += cross(g[i], g[ (i + 1) % n ]);
	return abs(ret) / 2.0;
}

int main(){
	int n, m;
	while(cin >> n >> m, n){
		Polygon g(n);
		rep(i,n){
			double a, b;
			cin >> a >> b;
			g[i] = Point(a,b);
		}

		vector<Point> v(m);
		rep(i,m){
			double a, b;
			cin >> a >> b;
			v[i] = Point(a,b);
		}

		rep(i,m){
			cout << fixed << setprecision(5) << areaOfPolygon(voronoiCell(g, v, i)) << endl;
		}
	}
}