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"

using namespace std;

using ll = long long;
using ld = long double;
using P = pair<int, int>;
constexpr ld EPS = 1e-12;
constexpr int INF = numeric_limits<int>::max() / 2;
constexpr int MOD = 1e9 + 7;

#define REP(i, n) for (int i = 0; i < (int)(n); i++)
#define ALL(x) (x).begin(), (x).end()

template <typename T>
void printv(const vector<T> &v)
{
    int sz = v.size();
    for (int i = 0; i < sz; i++)
    {
        cout << v[i] << " \n"[i == sz - 1];
    }
}

using Point = complex<ld>;

const ld eps = 1e-9, pi = acos(-1.0);

namespace std
{
bool operator<(const Point &lhs, const Point &rhs)
{
    if (lhs.real() < rhs.real() - eps)
        return true;
    if (lhs.real() > rhs.real() + eps)
        return false;
    return lhs.imag() < rhs.imag();
}
} // namespace std

Point input_point()
{
    ld x, y;
    cin >> x >> y;
    return Point(x, y);
}

bool eq(ld a, ld b)
{
    return (abs(a - b) < eps);
}

ld dot(Point a, Point b)
{
    return real(conj(a) * b);
}

ld cross(Point a, Point b)
{
    return imag(conj(a) * b);
}

class Line
{
  public:
    Point a, b;
    Line() : a(Point(0, 0)), b(Point(0, 0)) {}
    Line(Point a, Point b) : a(a), b(b) {}
};

class Circle
{
  public:
    Point p;
    ld r;
    Circle() : p(Point(0, 0)), r(0) {}
    Circle(Point p, ld r) : p(p), r(r) {}
};

// CCW::counter clockwise
int ccw(Point a, Point b, Point c)
{
    b -= a;
    c -= a;
    if (cross(b, c) > eps)
        return 1; // a,b,c : counter-clockwise
    if (cross(b, c) < -eps)
        return -1; // a,b,c : clockwise
    if (dot(b, c) < 0)
        return 2; // c,a,b : on a line
    if (norm(b) < norm(c))
        return -2; // a,b,c : on a line
    return 0;      // a,c,b : on a line
}

bool isis_ll(Line l, Line m)
{
    return !eq(cross(l.b - l.a, m.b - m.a), 0);
}

// s : line segment
bool isis_ls(Line l, Line s)
{
    return isis_ll(l, s) &&
           (cross(l.b - l.a, s.a - l.a) * cross(l.b - l.a, s.b - l.a) < eps);
}

bool isis_ss(Line s, Line t)
{
    return ccw(s.a, s.b, t.a) * ccw(s.a, s.b, t.b) <= 0 &&
           ccw(t.a, t.b, s.a) * ccw(t.a, t.b, s.b) <= 0;
}

bool isis_lp(Line l, Point p)
{
    return (abs(cross(l.b - p, l.a - p)) < eps);
}

bool isis_sp(Line s, Point p)
{
    return (abs(s.a - p) + abs(s.b - p) - abs(s.b - s.a) < eps);
}

Point proj(Line l, Point p)
{
    ld t = dot(p - l.a, l.a - l.b) / norm(l.a - l.b);
    return l.a + t * (l.a - l.b);
}

Point is_ll(Line s, Line t)
{
    Point sv = s.b - s.a, tv = t.b - t.a;
    assert(cross(sv, tv) != 0);
    return s.a + sv * cross(tv, t.a - s.a) / cross(tv, sv);
}

ld dist_lp(Line l, Point p)
{
    return abs(p - proj(l, p));
}

ld dist_ll(Line l, Line m)
{
    return isis_ll(l, m) ? 0 : dist_lp(l, m.a);
}

ld dist_ls(Line l, Line s)
{
    return isis_ls(l, s) ? 0 : min(dist_lp(l, s.a), dist_lp(l, s.b));
}

ld dist_sp(Line s, Point p)
{
    Point r = proj(s, p);
    return isis_sp(s, r) ? abs(r - p) : min(abs(s.a - p), abs(s.b - p));
}

ld dist_ss(Line s, Line t)
{
    if (isis_ss(s, t))
        return 0;
    return min({dist_sp(s, t.a), dist_sp(s, t.b), dist_sp(t, s.a), dist_sp(t, s.b)});
}

vector<Point> is_cc(Circle c1, Circle c2)
{
    vector<Point> res;
    ld d = abs(c1.p - c2.p);
    ld rc = (d * d + c1.r * c1.r - c2.r * c2.r) / (2 * d);
    ld dfr = c1.r * c1.r - rc * rc;
    if (abs(dfr) < eps)
        dfr = 0.0;
    else if (dfr < 0.0)
        return res; // no intersection
    ld rs = sqrt(dfr);
    Point diff = (c2.p - c1.p) / d;
    res.push_back(c1.p + diff * Point(rc, rs));
    if (dfr != 0.0)
        res.push_back(c1.p + diff * Point(rc, -rs));
    return res;
}

vector<Point> is_lc(Circle c, Line l)
{
    vector<Point> res;
    ld d = dist_lp(l, c.p);
    if (d < c.r + eps)
    {
        ld len = (d > c.r) ? 0.0 : sqrt(c.r * c.r - d * d); //safety;
        Point nor = (l.a - l.b) / abs(l.a - l.b);
        res.push_back(proj(l, c.p) + len * nor);
        res.push_back(proj(l, c.p) - len * nor);
    }
    return res;
}

vector<Point> is_sc(Circle c, Line l)
{
    vector<Point> v = is_lc(c, l), res;
    for (Point p : v)
        if (isis_sp(l, p))
            res.push_back(p);
    return res;
}

vector<Line> tangent_cp(Circle c, Point p)
{
    vector<Line> ret;
    Point v = c.p - p;
    ld d = abs(v);
    ld l = sqrt(norm(v) - c.r * c.r);
    if (isnan(l))
    {
        return ret;
    }
    Point v1 = v * Point(l / d, c.r / d);
    Point v2 = v * Point(l / d, -c.r / d);
    ret.push_back(Line(p, p + v1));
    if (l < eps)
        return ret;
    ret.push_back(Line(p, p + v2));
    return ret;
}

vector<Line> tangent_cc(Circle c1, Circle c2)
{
    vector<Line> ret;
    if (abs(c1.p - c2.p) - (c1.r + c2.r) > -eps)
    {
        Point center = (c1.p * c2.r + c2.p * c1.r) / (c1.r + c2.r);
        ret = tangent_cp(c1, center);
    }
    if (abs(c1.r - c2.r) > eps)
    {
        Point out = (-c1.p * c2.r + c2.p * c1.r) / (c1.r - c2.r);
        vector<Line> nret = tangent_cp(c1, out);
        ret.insert(ret.end(), ALL(nret));
    }
    else
    {
        Point v = c2.p - c1.p;
        v /= abs(v);
        Point q1 = c1.p + v * Point(0, 1) * c1.r;
        Point q2 = c1.p + v * Point(0, -1) * c1.r;
        ret.push_back(Line(q1, q1 + v));
        ret.push_back(Line(q2, q2 + v));
    }
    return ret;
}

typedef vector<Point> Polygon;

ld area(const Polygon &p)
{
    ld res = 0;
    int n = p.size();
    REP(j, n)
    res += cross(p[j], p[(j + 1) % n]);
    return res / 2;
}

bool is_counter_clockwise(const Polygon &poly)
{
    ld angle = 0;
    int n = poly.size();
    REP(i, n)
    {
        Point a = poly[i], b = poly[(i + 1) % n], c = poly[(i + 2) % n];
        angle += arg((c - b) / (b - a));
    }
    return angle > eps;
}

// -1 => out
//  0 => on
//  1 => in
int is_in_polygon(const Polygon &poly, Point p)
{
    ld angle = 0;
    int n = poly.size();
    REP(i, n)
    {
        Point a = poly[i], b = poly[(i + 1) % n];
        if (isis_sp(Line(a, b), p))
            return 1;
        angle += arg((b - p) / (a - p));
    }
    return eq(angle, 0) ? 0 : 2;
}

Polygon convex_hull(vector<Point> ps)
{
    int n = ps.size();
    int k = 0;
    sort(ps.begin(), ps.end());
    Polygon ch(2 * n);
    for (int i = 0; i < n; ch[k++] = ps[i++])
        while (k >= 2 && ccw(ch[k - 2], ch[k - 1], ps[i]) <= 0)
            --k;
    for (int i = n - 2, t = k + 1; i >= 0; ch[k++] = ps[i--])
        while (k >= t && ccw(ch[k - 2], ch[k - 1], ps[i]) <= 0)
            --k;
    ch.resize(k - 1);
    return ch;
}

Polygon convex_cut(const Polygon &ps, Line l)
{
    int n = ps.size();
    Polygon Q;
    REP(i, n)
    {
        Point A = ps[i], B = ps[(i + 1) % n];
        Line m = Line(A, B);
        if (ccw(l.a, l.b, A) != -1)
            Q.push_back(A);
        if (ccw(l.a, l.b, A) * ccw(l.a, l.b, B) < 0 && isis_ll(l, m))
            Q.push_back(is_ll(l, m));
    }
    return Q;
}

// a, b の垂直二等分線. a -> b を90度反時計回り回転
Line bisector(Point a, Point b)
{
    Point mid = (a + b) * Point(0.5, 0);
    return Line(mid, mid + (b - a) * Point(0, pi / 2));
}

int main()
{
    cin.tie(0);
    ios::sync_with_stdio(false);

    int N, M;
    while (cin >> N >> M, N || M)
    {
        Polygon island;
        for (int i = 0; i < N; i++)
        {
            ld x, y;
            cin >> x >> y;
            island.push_back(Point(x, y));
        }
        vector<Point> castle;
        for (int i = 0; i < M; i++)
        {
            ld x, y;
            cin >> x >> y;
            castle.push_back(Point(x, y));
        }
        for (int i = 0; i < M; i++)
        {
            Polygon p = island;
            for (int j = 0; j < M; j++)
            {
                if (i == j)
                    continue;
                Line l = bisector(castle[i], castle[j]);
                p = convex_cut(p, l);
            }
            cout << fixed << setprecision(10) << area(p) << endl;
        }
    }
}