### Problem Statement### 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.

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.

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.

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

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