Mixing Waters: Find the k-th Highest Temperature

You are given n cups of water. The i-th cup contains water with temperature \(c_i\) and volume \(a_i\). When mixing any two cups, the temperature of the resulting water will be computed using the formula:

\(T = \frac{c_i \times a_i + c_j \times a_j}{a_i + a_j}\)

No heat is lost during the mixing process.

Your task is to determine the k-th highest temperature value among all possible mixtures of two distinct cups.

Note: Please ensure that your answer retains at least 3 decimal places. The answer is considered correct if it differs from the standard answer by no more than \(10^{-2}\).

inputFormat

The first line contains two integers n and k (\(2 \le n\le 10^3\) for example, though constraints are not strictly specified), separated by a space.

Each of the following n lines contains two real numbers: ci (temperature) and ai (volume) for the i-th cup.

outputFormat

Output the k-th highest temperature value among all mixtures of any two cups. The result should be printed with at least 3 decimal places.

sample

3 1
30 1
20 1
10 1

25.000