P6733 "Wdsr-2" Geyser.

**Problem Number:** $\textit{08}$

There is a geyser that produced $n$ cups of water. For some reasons, each cup has a different temperature and volume. The temperature of the $i$-th cup is $c_i$, and the volume is $a_i$. Now mix any **two** cups of water. Each time you mix two cups, you will get a new temperature value. Find the $k$-th highest possible temperature value (ignoring heat loss). **It is recommended that your answer keep at least $\bm 3$ digits after the decimal point (it will be accepted if the difference from the standard answer is within $\bm{10^{-2}}$).**

The first line contains two integers $n, k$, as described above. The next $n$ lines each contain two numbers $a_i, c_i$.

Output one real number, representing the $k$-th highest temperature after mixing.

#### Explanation for Sample 1 Mixing the $1$-st and the $5$-th cups gives a temperature value of $4.5$. It can be seen that this is the highest possible water temperature. #### Sample 2 See the attached files $\textbf{\textit{pour2.in/pour2.ans}}$. #### Constraints and Notes **This problem uses bundled testdata.** - $\textbf{Subtask 1}\text{ (10 pts)}$: $1\le n\le 10$. - $\textbf{Subtask 2}\text{ (40 pts)}$: guaranteed $k=1$. - $\textbf{Subtask 3}\text{ (50 pts)}$: no special restrictions. - $\textbf{Subtask 4}\text{ (0 pts)}$: hack testdata. For $100\%$ of the data: $1\le n\le 10^5$, $1\le k\le \dfrac{n \times (n - 1)}{2}$, $1\le a_i,c_i\le 10^9$. The time limit is $\text{2 s}$ for Subtasks 2/3/4, and $\text{1 s}$ for Subtask 1. #### Prerequisite Knowledge For two cups of water with volume and temperature $(a_i,c_i),(a_j,c_j)$, the temperature after mixing is: $$ T=\dfrac{a_ic_i+a_jc_j}{a_i+a_j} $$ #### Note The testdata of this problem is generated using [SvRan](https://github.com/Sept0913/SvRan), taking only $3\min$. Translated by ChatGPT 5