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 P₂is 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.

Figure I.1: Cross sections of Prisms

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.

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 
.
.
.
x_1m y_1m 
x₂₁ z₂₁
x₂₂ z₂₂
.
.
.
x_2n z_2n

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.

x_1i, y 1 i, x _2j and z _2j are integers between -100 and 100, inclusive. ( x _1i, y _1i) and ( x _2j , z _2j) mean the i-th and j-th vertices' positions of C ₁ and C ₂respectively.

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.

Sample 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 for the Sample Input

4.708333333333333
1680.0000000000005
491.1500000000007
0.0
7600258.4847715655

Simpson公式就是在数值积分中用二次函数来近似原函数进行积分而得到的公式，如果原函数本身就是次数不超过二的多项式，那么用Simpson公式就可以得到精确的积分值。利用该公式，无需求出关于x的多项式，而只要计算按区间的端点和中点切片得到的长方形的面积就够了。