Hongjun's matrix

Hongjun has two sequences $A$ and $B$, each of length $N$. He builds an $N \times N$ matrix whose entry in row $i$ and column $j$ is $A_i \times B_j$.

Hongjun sorts all $N^2$ entries in non-decreasing order and wants to know the value that lands in position $K$. Positions are counted from 1, and a value that appears several times is counted once for each entry that produces it. Write the program that finds the $K$-th value for him, since sorting is slow for Hongjun.

The first line contains $N$ and $K$, separated by a space. ($1 \le N \le 30000$, $1 \le K \le N^2$)

The second line contains the $N$ elements of the sequence $A$, separated by spaces.

The third line contains the $N$ elements of the sequence $B$, separated by spaces.

Every element of both sequences is an integer between $1$ and $10^9$.

Print the $K$-th smallest entry of the matrix.