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ZOJ Problem Set - 3278
8G Island

Time Limit: 3 Seconds      Memory Limit: 32768 KB

8g Island has N boys and M girls. Every person has a "charm value". When a boy with charm value t1 and a girl with charm value t2 get together, their "8g value" is t1*t2. Every year the king will choose the Kth greatest number from all the N*M possible 8g values as the lucky number of the year. People on the island knows nothing but 8g, so they ask you to help them find the lucky number.

Input

The input contains multiply test cases(<= 10). Each test case contains three parts:

    1 Three integers N, M(1 <= N,M <= 100000) and K(1 <= K <= N*M) in a line, as mentioned above.

    2 N integers in a line, the charm value of each boy.

    3 M integers in a line, the charm value of each girl.

    All the charm values are integers between 1 and 100000(inclusive).

Process to the end-of-file.

Output

For each test case print a single line that contains the lucky number.

Sample Input

3 2 3
1 2 3
1 2

2 2 1
1 1
1 1

2 2 4
1 1
1 1

Sample Output

3
1
1

Author: WANG, Yelei
Source: ZOJ Monthly, December 2009
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