Octorber 1 is the Kindergarten Day on which college students volunteer to work at kindergartens across the country. As you have gathered the kids you decide to assign them some mission impossible so that you can take a nap. You gave them a huge pile of numbers and ask them to sort them from the biggest to the smallest, and pick the kth number for you.
What amazed you most is that the kids took out their notebooks to start programming. You realized they would come back in a while for the answers. As there are a few kids you need a program that beats their sorting program (whatever algorithm it depends on).
Input
Each case starts by two integers n and m, where n*n is the number of integers you gave them, and m is the number of kids (each of them is assigned a different k). (0 < n <= 1000, 0 < m <= 20)
The second line contains n integers, and the original data is obtained by multiple each pair of the n numbers. (Yes they could overflow, but just rely on the overflow behavior of a 32-bit signed integer).
The third line contains m integers, each of which in the range from 1 to n*n, which are the tasks you assigned the kids.
A case with n = 0 terminates the input.
Output
For each test case print m numbers on a single line separated by a space, which are the answers for the m kids.
Sample Input
1 1
1
1
2 2
1 2
2 4
0 0
Sample Output
1
2 1
