Problem Description

Takahashi decided to improve his computational skills with "100 Million Square Calculation." This involves creating a table with $ N $ rows and $ N $ columns. For the $ i $-th row, the number $ a_i $ is written to the left of the leftmost cell, and for the $ j $-th column, the number $ b_j $ is written above the topmost cell. Takahashi calculates and fills in the value of $a_i \times b_j$ in the cell at the $ i $-th row and $ j $-th column.

Bored with the quick completion, Takahashi decided to sort the $ N^2 $ values he wrote in ascending order. Find the value that is at the $ K $-th position (starting from 1) in this sorted list.

Input Format

The input is given from the standard input in the following format:

$ N $ $ K $ $ a_1 $ $ a_2 $ .. $ a_N $ $ b_1 $ $ b_2 $ .. $ b_N $

• The first line contains the number of rows and columns of the table $ N $ ($1 \leq N \leq 30000$) and the position $ K $ ($1 \leq K \leq N^2$) in the sorted list to find, separated by spaces.
• The second line contains the numbers $ a_i $ ($1 \leq a_i \leq 10^9$) written to the left of the leftmost cell of each row $ i $ ($1 \leq i \leq N$), separated by spaces.
• The third line contains the numbers $ b_j $ ($1 \leq b_j \leq 10^9$) written above the topmost cell of each column $ j $ ($1 \leq j \leq N$), separated by spaces.

Output Format

Output to the standard output the value that is at the $ K $-th position (starting from 1) in the sorted list of the $ N^2 $ values written by Takahashi, followed by a newline.

Sample Input and Output

Sample Input #1

2 3
2 3
3 5

Sample Output #1

10

Sample Input #2

3 7
1 2 1
2 1 2

Sample Output #2

2

Sample Input #3

4 8
701687787 500872619 516391519 599949380
458299111 633119409 377269575 717229869

Sample Output #3

317112176525562171

Notes/Hints

Partial Points

This problem has partial points.

• Test cases worth 5 points satisfy $1 \leq N \leq 10$.

Sample Explanation 1

After sorting the values written by Takahashi in ascending order, we get $ 6, 9, 10, 15 $, and the 3rd smallest value is $ 10 $.

Sample Explanation 2

After sorting the values written by Takahashi in ascending order, we get $ 1, 1, 2, 2, 2, 2, 2, 4, 4 $, and the 7th smallest value is $ 2 $.

见题面 Input 部分

见题面 Output 部分