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1 초 128 MB 1 1 1 100.000%

문제

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.

C1 : Cross section of P1 and the xy-plane(Left) C2 : Cross section of P2 and the xz-plane(Right)

Figure I.1: Cross sections of Prisms

P1 and C1(Left) P2 and C2(Right)

Figure I.2: Prisms and their cross sections

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.

입력

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.

출력

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.

예제 입력

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

예제 출력

4.708333333333333
1680.0000000000005
491.1500000000007
0.0
7600258.4847715655

힌트