Intersection of Two Prisms

Suppose that $P_1$ is a prism of infinite height whose axis is parallel to the $z$-axis, and $P_2$ is also a prism of infinite height whose axis is parallel to the $y$-axis. $P_1$ is defined by the polygon $C_1$, which is the cross section of $P_1$ and the $xy$-plane, and $P_2$ is defined by the polygon $C_2$, which is the cross section of $P_2$ and the $xz$-plane.

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

$C_1$: cross section of $P_1$ and the $xy$-plane (left). $C_2$: cross section of $P_2$ and the $xz$-plane (right).

Figure I.1: Cross sections of the prisms.

$P_1$ and $C_1$ (left). $P_2$ and $C_2$ (right).

Figure I.2: Prisms and their cross sections.

Figure I.3: Intersection of the two prisms.

Figure I.3 shows the intersection of the two prisms in Figure I.2, namely $P_1$ and $P_2$.

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

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 ($3 \le m \le 100$, $3 \le n \le 100$) that represent the numbers of vertices of the polygons $C_1$ and $C_2$, respectively.

$x_{1i}$, $y_{1i}$, $x_{2j}$ and $z_{2j}$ are integers between $-100$ and $100$, inclusive. $(x_{1i}, y_{1i})$ and $(x_{2j}, z_{2j})$ are the positions of the $i$-th and $j$-th vertices of $C_1$ and $C_2$, respectively.

The sequences of these vertex positions are given in 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 interior angles of each polygon are less than 180 degrees. You may also assume that all the polygons are simple; that is, each polygon's boundary neither crosses nor touches itself.

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

For each dataset, output the exact volume of the intersection of the two prisms $P_1$ and $P_2$ on its own line. Because all vertex coordinates are integers, this volume is always a rational number. Print it as a fraction p/q in lowest terms, where $q > 0$ and $p$ and $q$ share no common factor greater than $1$ (an integer volume $V$ is written as V/1, and a volume of zero is written as 0/1). Do not print any other characters.