Problem Statement

Takahashi and Aoki have N and M bottles of sugar water, respectively.
Takahashi's i-th sugar water is composed of A_i grams of sugar and B_i grams of water.
Aoki's i-th sugar water is composed of C_i grams of sugar and D_i grams of water.
There are NM ways to choose one from Takahashi's sugar waters and one from Aoki's and mix them. Among the NM sugar waters that can be obtained in this way, find the concentration of sugar in the sugar water with the K-th highest concentration of sugar.
Here, the concentration of sugar in sugar water composed of x grams of sugar and y grams of water is $\dfrac{100x}{x+y}$ percent. We will ignore saturation.

Input

The input is given from Standard Input in the following format:
N M K
A_1 B_1
A_2 B_2
$\vdots$
A_N B_N
C_1 D_1
C_2 D_2
$\vdots$
C_M D_M

Output

Print the concentration of sugar in the sugar water with the K-th highest concentration of sugar in percent.
Your output will be considered correct if the absolute or relative error from the true value is at most 10^{−9}.

Constraints

• $1 \leq N, M \leq 5 \times 10^4$
• $1 \leq K \leq N \times M$
• $1 \leq A_i, B_i, C_i, D_i \leq 10^5$
• All values in the input are integers.

Sample Input 1

3 1 1
1 2
4 1
1 4
1 4

Sample Output 1

50.000000000000000

Let (i, j) denote the sugar water obtained by mixing Takahashi's i-th sugar water and Aoki's j-th.
Below are the sugar waters that can be obtained and their concentrations of sugar.

• (1, 1) : $100 \times \frac{1 + 1}{(1 + 1) + (2 + 4)} = 25$ \%
• (2, 1) : $100 \times \frac{1 + 4}{(4 + 1) + (1 + 4)} = 50$ \%
• (3, 1) : $100 \times \frac{1 + 1}{(1 + 1) + (4 + 4)} = 20$ \%

Among them, the sugar water with the highest concentration of sugar is (2, 1), with a concentration of 50 percent.

Sample Input 2

2 2 2
6 4
10 1
5 8
9 6

Sample Output 2

62.500000000000000

Sample Input 3

4 5 10
5 4
1 6
7 4
9 8
2 2
5 6
6 7
5 3
8 1

Sample Output 3

54.166666666666664

见题面 Input 部分

见题面 Output 部分