Problem: Suppose that P1 is an infinite-height prism whose axis is parallel to the z-axis, and P2 is also an infinite-height prism whose axis is parallel to the y-axis. P1 is defined by the polygon C1 which is the cross section of P1 and the xy-plane, and P2 is also defined by the polygon C2 which is the cross section of P2 and the xz-plane.

Figure I.1 shows two cross sections which appear as the first dataset in the sample input, and Figure I.2 shows the relationship between the prisms and their cross sections.

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Figure I.1: Cross sections of Prisms

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Figure I.2: Prisms and their cross sections

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Figure I.3: Intersection of two prisms

Figure I.3 shows the intersection of two prisms in Figure I.2, namely, P1 and P2.

Write a program which calculates the volume of the intersection of two prisms.



Input

The input is a sequence of datasets. The number of datasets is less than 200.

Each dataset is formatted as follows.

m n
x11 y11
x12 y12
.
.
.
x1m y1m
x21 z21
x22 z22
.
.
.
x2n z2n


m and n are integers (3 ≤ m ≤ 100, 3 ≤ n ≤ 100) which represent the numbers of the vertices of the polygons, C1 and C2, respectively.

x1i, y1i, x2j and z2j are integers between -100 and 100, inclusive. (x1i, y1i) and (x2j , z2j) mean the i-th and j-th vertices' positions of C1 and C2 respectively.

The sequences of these vertex positions are given in the counterclockwise order either on the xy-plane or the xz-plane as in Figure I.1.

You may assume that all the polygons are convex, that is, all the interior angles of the polygons are less than 180 degrees. You may also assume that all the polygons are simple, that is, each polygon's boundary does not cross nor touch itself.

The end of the input is indicated by a line containing two zeros.

Output

For each dataset, output the volume of the intersection of the two prisms, P1 and P2, with a decimal representation in a line.

None of the output values may have an error greater than 0.001. The output should not contain any other extra characters.

Example

Input

4 3
7 2
3 3
0 2
3 1
4 2
0 1
8 1
4 4
30 2
30 12
2 12
2 2
15 2
30 8
13 14
2 8
8 5
13 5
21 7
21 9
18 15
11 15
6 10
6 8
8 5
10 12
5 9
15 6
20 10
18 12
3 3
5 5
10 3
10 10
20 8
10 15
10 8
4 4
-98 99
-99 -99
99 -98
99 97
-99 99
-98 -98
99 -99
96 99
0 0


Output

4.708333333333333
1680.0000000000005
491.1500000000007
0.0
7600258.4847715655

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;

template<class T> inline void chmin(T &a, const T &b) { if(a > b) a = b; }
template<class T> inline void chmax(T &a, const T &b) { if(a < b) a = b; }

typedef double Real;
constexpr Real EPS = 1e-8;
inline int sign(Real d) { return d > EPS ? 1 : d < -EPS ? -1 : 0; }

struct Point {
	Real x, y;
	explicit Point(Real x_ = 0, Real y_ = 0):x(x_), y(y_) {}
	Point operator+(const Point &p) const { return Point(x + p.x, y + p.y); }
	Point operator-(const Point &p) const { return Point(x - p.x, y - p.y); }
	Point operator*(Real s) const { return Point(x * s, y * s); }
	bool operator<(const Point &p) const { return sign(x - p.x) == -1 || (sign(x - p.x) == 0 && sign(y - p.y) == -1); }
	bool operator==(const Point &p) const { return sign(x - p.x) == 0 && sign(y - p.y) == 0; }
};

inline istream &operator>>(istream &is, Point &p) {
	return is >> p.x >> p.y;
}

struct Segment : public array<Point, 2> {
	Segment(const Point &a, const Point &b) { at(0) = a; at(1) = b; }
};

typedef vector<Point> Polygon;

inline Real norm(const Point &p) {
	return p.x * p.x + p.y * p.y;
}

inline Real abs(const Point &p) {
	return sqrt(norm(p));
}

inline Real dot(const Point &a, const Point &b) {
	return a.x * b.x + a.y * b.y;
}

inline Real cross(const Point &a, const Point &b) {
	return a.x * b.y - a.y * b.x;
}

enum { CCW = 1, CW = -1, BACK = 2, FRONT = -2, ON = 0};
inline int ccw(const Point &a, const Point &b, const Point &c) {
	const Point p = b - a;
	const Point q = c - a;
	const int sign_cross = sign(cross(p, q));

	if(sign_cross == 1) return CCW;
	if(sign_cross == -1) return CW;
	if(sign(dot(p, q)) == -1) return BACK;
	if(sign(norm(p) - norm(q)) == -1) return FRONT;
	return ON;
}

inline bool intersect(const Segment &s, const Point &p) {
	return ccw(s[0], s[1], p) == ON;
}

inline bool intersect(const Segment &a, const Segment &b) {
	return ccw(a[0], a[1], b[0]) * ccw(a[0], a[1], b[1]) <= 0
		&& ccw(b[0], b[1], a[0]) * ccw(b[0], b[1], a[1]) <= 0;
}

inline Real dist(const Point &a, const Point &b) {
	return abs(a - b);
}

inline Point crosspoint(const Segment &a, const Segment &b) {
	const Real crs = cross(a[1] - a[0], b[1] - b[0]);
	if(sign(crs) == 0) {
		if(intersect(a, b[0])) return b[0];
		if(intersect(a, b[1])) return b[1];
		if(intersect(b, a[0])) return a[0];
		return a[1];
	}
	return b[0] + (b[1] - b[0]) * (cross(a[1] - a[0], a[1] - b[0]) / crs);
}

// *solve

int main() {
	cin.tie(nullptr);
	ios::sync_with_stdio(false);
	cout.setf(ios::fixed);
	cout.precision(10);

	constexpr Real INF = 1e6;

	for(int m, n; cin >> m >> n && m;) {
		vector<Real> xs;
		Polygon c1(m), c2(n);
		Real L1 = INF, R1 = -INF, L2 = INF, R2 = -INF;

		for(auto &e : c1) {
			cin >> e;
			xs.emplace_back(e.x);
			chmin(L1, e.x);
			chmax(R1, e.x);
		}
		for(auto &e : c2) {
			cin >> e;
			xs.emplace_back(e.x);
			chmin(L2, e.x);
			chmax(R2, e.x);
		}

		const Real L = max(L1, L2), R = min(R1, R2);

		sort(begin(xs), end(xs));
		xs.erase(unique(begin(xs), end(xs)), end(xs));

		const auto width = [](const Polygon &p, Real x) {
			Segment cut(Point(x, INF), Point(x, -INF));
			Real low = INF, high = -INF;
			Point prev = p.back();

			for(const auto &curr : p) {
				const Segment edge(prev, curr);
				if(intersect(edge, cut)) {
					const auto cp = crosspoint(edge, cut);
					chmin(low, cp.y);
					chmax(high, cp.y);
				}
				prev = curr;
			}
			return max(0.0, high - low);
		};
		const auto f = [&](Real x) { return width(c1, x) * width(c2, x); };
		const auto simpson = [&](Real a, Real b) {
			const Real c = (a + b) / 2;
			return L < c && c < R ? (b - a) / 6 * (f(a) + 4 * f(c) + f(b)) : 0;
		};

		Real ans = 0.0;
		for(int i = 1; i < xs.size(); ++i) {
			ans += simpson(xs[i - 1], xs[i]);
		}
		cout << ans << endl;
	}

	return EXIT_SUCCESS;
}