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:
// Enjoy your stay.

#include <bits/stdc++.h>

#define EPS 1e-9
#define INF 1070000000LL
#define MOD 1000000007LL
#define fir first
#define foreach(it,X) for(auto it=(X).begin();it!=(X).end();it++)
#define ite iterator
#define mp make_pair
#define mt make_tuple
#define rep(i,n) rep2(i,0,n)
#define rep2(i,m,n) for(int i=m;i<(n);i++)
#define pb push_back
#define sec second
#define sz(x) ((int)(x).size())

using namespace std;

typedef istringstream iss;
typedef long long ll;
typedef pair<ll,ll> pi;
typedef stringstream sst;
typedef vector<ll> vi;

// geometry library from hos

const double PI = acos(-1);

int sig(double r) { return (r < -EPS) ? -1 : (r > +EPS) ? +1 : 0; }

struct Pt{
	double x, y;
	Pt() {}
	Pt(double x, double y) : x(x), y(y) {}
	Pt operator+(const Pt &a) const { return Pt(x + a.x, y + a.y); }
	Pt operator-(const Pt &a) const { return Pt(x - a.x, y - a.y); }
	Pt operator*(const Pt &a) const { return Pt(x * a.x - y * a.y, x * a.y + y * a.x); }
	Pt operator-() const { return Pt(-x, -y); }
	Pt operator*(const double &k) const { return Pt(x * k, y * k); }
	Pt operator/(const double &k) const { return Pt(x / k, y / k); }
	double abs() const { return sqrt(x * x + y * y); }
	double abs2() const { return x * x + y * y; }
	double arg() const { return atan2(y, x); }
	double dot(const Pt &a) const { return x * a.x + y * a.y; }
	double det(const Pt &a) const { return x * a.y - y * a.x; }
	bool operator<(const Pt &a) const { return x < a.x || x == a.x && y < a.y; }
	bool operator==(const Pt &a) const { return x == a.x && y == a.y; }
	bool operator!=(const Pt &a) const { return x != a.x || y != a.y; }
};

ostream &operator<<(ostream &os, const Pt &a) { os << "(" << a.x << ", " << a.y << ")"; return os; }

double tri(const Pt &a, const Pt &b, const Pt &c) { return (b - a).det(c - a); }

int iSP(Pt a, Pt b, Pt c) {
	int s = sig((b - a).det(c - a));
	if (s) return s; // +1 or -1
	if (sig((b - a).dot(c - a)) < 0) return -2; // c-a-b
	if (sig((a - b).dot(c - b)) < 0) return +2; // a-b-c
	return 0;
}
int iLL(Pt a, Pt b, Pt c, Pt d) {
	if (sig((b - a).det(d - c))) return 1; // intersect
	if (sig((b - a).det(c - a))) return 0; // parallel
	return -1; // correspond
}
bool iLS(Pt a, Pt b, Pt c, Pt d) {
	return (sig(tri(a, b, c)) * sig(tri(a, b, d)) <= 0);
}
bool iSS(Pt a, Pt b, Pt c, Pt d) {
	return (iSP(a, b, c) * iSP(a, b, d) <= 0 && iSP(c, d, a) * iSP(c, d, b) <= 0);
}
bool iSSstrict(Pt a, Pt b, Pt c, Pt d) {
	return (sig(tri(a, b, c)) * sig(tri(a, b, d)) < 0 && sig(tri(c, d, a)) * sig(tri(c, d, b)) < 0);
}
Pt pLL(Pt a, Pt b, Pt c, Pt d) { // intersection
	b = b - a; d = d - c; return a + b * (c - a).det(d) / b.det(d);
}
double dLP(Pt a, Pt b, Pt c) {
	return abs(tri(a, b, c)) / (b - a).abs();
}
double dSP(Pt a, Pt b, Pt c) {
	if (sig((b - a).dot(c - a)) <= 0) return (c - a).abs();
	if (sig((a - b).dot(c - b)) <= 0) return (c - b).abs();
	return abs(tri(a, b, c)) / (b - a).abs();
}
double dLL(Pt a, Pt b, Pt c, Pt d) {
	return iLL(a, b, c, d) ? 0 : dLP(a, b, c);
}
double dLS(Pt a, Pt b, Pt c, Pt d) {
	return iLS(a, b, c, d) ? 0 : min(dLP(a, b, c), dLP(a, b, d));
}
double dSS(Pt a, Pt b, Pt c, Pt d) {
	return iSS(a, b, c, d) ? 0 : min(min(dSP(a, b, c), dSP(a, b, d)), min(dSP(c, d, a), dSP(c, d, b)));
}

int iCC(Pt a, double r, Pt b, double s) {
	double d = (b - a).abs();
	if (sig(d) == 0 && sig(r - s) == 0) return -1; // correspond
	if (sig(r - s - d) > 0) return +2; // r > s
	if (sig(s - r - d) > 0) return -2; // s > r
	return (sig(r + s - d) >= 0) ? 1 : 0;
}
bool iCS(Pt a, double r, Pt b, Pt c) {
	return (sig(r - dSP(b, c, a)) >= 0 && sig(r - max((b - a).abs(), (c - a).abs())) <= 0);
}
pair<Pt,Pt> pCC(Pt a, double r, Pt b, double s) {
	double d = (b - a).abs();
	double x = (d * d + r * r - s * s) / (d * 2);
	Pt e = (b - a) / d, w = e * Pt(0, 1) * sqrt(max(r * r - x * x, 0.0));
	return mp(a + e * x - w, a + e * x + w);
}
pair<Pt,Pt> pCL(Pt a, double r, Pt b, Pt c) {
	Pt h = b + (c - b) * (c - b).dot(a - b) / (c - b).abs2();
	// perp(b, c, a)
	double d = (h - a).abs();
	double y = sqrt(max(r * r - d * d, 0.0));
	Pt e = (c - b) / (c - b).abs();
	return mp(h - e * y, h + e * y);
}
pair<Pt,Pt> tCP(Pt a, double r, Pt b) {
	double d2 = (b - a).abs2();
	double x = sqrt(max(d2 - r * r, 0.0));
	Pt h = a + (b - a) * (r * r / d2);
	Pt w = (b - a) * Pt(0, 1) * (x * r / d2);
	return mp(h - w, h + w);
}
double aCC(Pt a, double r, Pt b, double s) {
	double d = (a - b).abs();
	if (sig(r - s - d) >= 0) return s * s * PI;
	if (sig(s - r - d) >= 0) return r * r * PI;
	if (sig(r + s - d) <= 0) return 0;
	double x = (d * d + r * r - s * s) / (d * 2);
	double h = sqrt(r * r - x * x);
	return r * r * atan2(h, x) + s * s * atan2(h, d - x) - d * h;
}

int convexHull(int n, Pt p[], Pt q[]){ // can replace sig&tri, <= with iSP, <
	int m=0, i, r;
	sort(p, p+n);
	for(i=0;        i<n;  q[m++]=p[i++]) for(; m>1 && sig(tri(q[m-2], q[m-1], p[i])) <= 0; --m);
	for(i=n-2, r=m; i>=0; q[m++]=p[i--]) for(; m>r && sig(tri(q[m-2], q[m-1], p[i])) <= 0; --m);
	return m-1;
}

int convexCut(int n, Pt p[], Pt a, Pt b, Pt q[]){
	int m=0, i;
	p[n] = p[0];
	rep(i, n){
		if(sig(tri(a, b, p[i])) >= 0) q[m++] = p[i];
		if(sig(tri(a, b, p[i])) * sig(tri(a, b, p[i+1])) < 0) q[m++] = pLL(a, b, p[i], p[i+1]);
	}
	q[m] = q[0];
	return m;
}

int sGP(int n, Pt p[], Pt a) {
	int side = -1, i;
	p[n] = p[0];
	for (i = 0; i < n; ++i) {
		Pt p0 = p[i] - a, p1 = p[i + 1] - a;
		if (sig(p0.det(p1)) == 0 && sig(p0.dot(p1)) <= 0) return 0;
		if (p0.y > p1.y) swap(p0, p1);
		if (sig(p0.y) <= 0 && 0 < sig(p1.y) && sig(p0.det(p1)) > 0) side = -side;
	}
	return side;
}
int sVP(int n, Pt p[], Pt a) {
	Pt o = (p[0] + p[n / 2]) / 2;
	int lo = 0, ho = n, fl = sig(tri(o, p[lo], a));
	p[n] = p[0];
	for (; lo + 1 < ho; ) {
		int mo = (lo + ho) / 2, fm = sig(tri(o, p[mo], a));
		(fl - fm - sig(tri(o, p[lo], p[mo])) < 0) ? (lo = mo, fl = fm) : ho = mo;
	}
	return sig(tri(p[lo], p[ho], a));
}

int sAP(Pt a, Pt b, Pt c) {
	return sig(a.det(c)) - sig(b.det(c)) - sig(a.det(b));
}

// end of library

int N,M;
Pt l[11],c[11];

int main2(){
	rep(i,M){
		int n=N;
		Pt p[33],q[33];
		rep(j,n)p[j]=l[j];
		rep(j,M)if(j!=i){
			Pt mid = (c[i]+c[j])/2;
			int m = convexCut(n,p,mid,mid+(c[j]-c[i])*Pt(0,1),q);
			n=m;
			rep(i,n)p[i]=q[i];
		}
		double res=0;
		rep(i,n)res+=p[i].det(p[(i+1)%n]);
		cout<<setprecision(16)<<res/2<<endl;
	}
	return 0;
}

int main(){
	while(cin>>N>>M,N){
		rep(i,N)cin>>l[i].x>>l[i].y;
		rep(i,M)cin>>c[i].x>>c[i].y;
		main2();
	}
}