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:
/*
Algorithm to determine the Voronoi diagrams of a set of points within a convex polygon that bounds the plane.

Time complexity: O((N + M)^2)
Space complexity: O(N + M)
*/

#include <cmath>

#include <iostream>
#include <iomanip>
#include <vector>
#include <algorithm>

#define x first
#define y second

using namespace std;

typedef pair<double, double> Point;

const double EPS = 1e-9;
const double PI = acos(-1.0);

class Line {
  public:
    double a, b, c;

    Line(const double _a = 0.0, const double _b = 0.0, const double _c = 0.0):
      a(_a),
      b(_b),
      c(_c) {}

    Line(const Point &p1, const Point &p2):
      a(p1.y - p2.y),
      b(p2.x - p1.x),
      c(p1.x * p2.y - p1.y * p2.x) {}
};

vector<Point> Plane, Points;
vector<double> Areas;

inline double Det(const Point &a, const Point &b, const Point &c) {
    return (b.x - a.x) * (c.y - a.y) - (b.y - a.y) * (c.x - a.x);
}

inline double Alpha(const Point &a, const Point &b, const Point &c) {
    Point u = Point(a.x - b.x, a.y - b.y), v = Point(c.x - b.x, c.y - b.y);
    double alpha = acos((u.x * v.x + u.y * v.y) / sqrt((u.x * u.x + u.y * u.y) * (v.x * v.x + v.y * v.y)));
    if (Det(a, b, c) < -EPS)
        alpha += 2 * PI;
    return alpha;
}

inline Point Dualize(const Line &l) {
    if (abs(l.c) < EPS)
        return Point(0.0, 0.0);
    return Point(l.a / l.c, l.b / l.c);
}

inline Line Dualize(const Point &p) {
    return Line(p.x, p.y, 0.0);
}

inline Point Translate(const Point &p, const Point &shift) {
    return Point(p.x + shift.x, p.y + shift.y);
}

inline Line Translate(const Line &l, const Point &shift) {
    return Line(l.a, l.b, l.c - l.a * shift.x - l.b * shift.y);
}

vector<Point> GetConvexHull(vector<Point> points) {
    int n = int(points.size()), origin = 0;
    for (int i = 1; i < n; ++i)
        if (points[i] < points[origin])
            origin = i;
    swap(points[0], points[origin]);
    vector<Point> hull;
    hull.push_back(points[0]);
    hull.push_back(points[1]);
    for (int i = 2; i < n; ++i)
        if (Det(hull[0], hull[1], points[i]) < -EPS)
            hull[1] = points[i];
    do {
        int next = -1;
        double alpha = -2 * PI;
        for (int i = 0; i < n; ++i) {
            double currentAlpha = Alpha(hull[int(hull.size()) - 2], hull[int(hull.size()) - 1], points[i]);
            if (currentAlpha > alpha) {
                next = i;
                alpha = currentAlpha;
            }
        }
        hull.push_back(points[next]);
    } while (hull.back() != hull.front());
    hull.pop_back();
    return hull;
}

vector< vector<Point> > GetVoronoiDiagrams(const vector<Point> &plane, const vector<Point> &points) {
    vector< vector<Point> > voronoiDiagrams = vector< vector<Point> >(int(points.size()), vector<Point>());
    for (int i = 0; i < int(points.size()); ++i) {
        Point shiftTo = Point(-points[i].x, -points[i].y), shiftFrom = points[i];
        vector<Point> dualizedLines;
        for (int j = 0; j < int(plane.size()); ++j)
            dualizedLines.push_back(Dualize(Translate(Line(plane[j], plane[(j + 1) % int(plane.size())]), shiftTo)));
        for (int j = 0; j < int(points.size()); ++j) {
            if (i != j) {
                Point a = points[i], b = points[j];
                dualizedLines.push_back(Dualize(Translate(Line(2 * (b.x - a.x), 2 * (b.y - a.y), a.x * a.x + a.y * a.y - b.x * b.x - b.y * b.y), shiftTo)));
            }
        }
        vector<Point> hull = GetConvexHull(dualizedLines);
        for (int j = 0; j < int(hull.size()); ++j)
            voronoiDiagrams[i].push_back(Translate(Dualize(Line(hull[j], hull[(j + 1) % int(hull.size())])), shiftFrom));
    }
    return voronoiDiagrams;
}

inline double Area(const vector<Point> &polygon) {
    double area = 0.0;
    for (int i = 0; i < int(polygon.size()); ++i)
        area += polygon[i].x * polygon[(i + 1) % int(polygon.size())].y - polygon[(i + 1) % int(polygon.size())].x * polygon[i].y;
    area *= 0.5;
    return abs(area);
}

void Solve() {
    vector< vector<Point> > voronoiDiagrams = GetVoronoiDiagrams(Plane, Points);
    Areas = vector<double>(int(Points.size()), 0.0);
    for (int i = 0; i < int(Points.size()); ++i)
        Areas[i] = Area(voronoiDiagrams[i]);
}

bool Read() {
    int m, n;
    cin >> m >> n;
    if (m == 0 && n == 0)
        return false;
    Plane = vector<Point>(m);
    for (int i = 0; i < m; ++i)
        cin >> Plane[i].x >> Plane[i].y;
    Points = vector<Point>(n);
    for (int i = 0; i < n; ++i)
        cin >> Points[i].x >> Points[i].y;
    return true;
}

void Print() {
    for (int i = 0; i < int(Points.size()); ++i)
        cout << fixed << setprecision(9) << Areas[i] << "\n";
}

int main() {
    while (Read()) {
        Solve();
        Print();
    }
    return 0;
}