Problem B: Black Box

Our Black Box represents a primitive database. It can save an integer array and has a special i variable. At the initial moment Black Box is empty and i equals 0. This Black Box processes a sequence of commands (transactions). There are two types of transactions:

  • ADD (x): put element x into Black Box;
  • GET: increase i by 1 and give an i-minimum out of all integers containing in the Black Box. Keep in mind that i-minimum is a number located at i-th place after Black Box elements sorting by non-descending.

    Let us examine a possible sequence of 11 transactions:

    N Transaction i     Black Box contents after transaction
    (elements are arranged by non-descending)     		Answer
    1 ADD (3) 0 3
    2 GET 1 3 3
    3 ADD (1) 1 1, 3
    4 GET 2 1, 3 3
    5 ADD (-4) 2 -4, 1, 3
    6 ADD (2) 2 -4, 1, 2, 3
    7 ADD (8) 2 -4, 1, 2, 3, 8
    8 ADD (-1000)   2 -1000, -4, 1, 2, 3, 8
    9 GET 3 -1000, -4, 1, 2, 3, 8 1
    10 GET 4 -1000, -4, 1, 2, 3, 8 2
    11 ADD (2) 4 -1000, -4, 1, 2, 2, 3, 8

    It is required to work out an efficient algorithm which treats a given sequence of transactions. The maximum number of ADD and GET transactions - 30000 of each type.

    Let us describe the sequence of transactions by two integer arrays:

    1. A(1), A(2), ..., A(M): a sequence of elements which are being included into Black Box. A values are integers not exceeding 2 000 000 000 by their absolute value, M<=30000 . For the Example 1 we have A=(3, 1, -4, 2, 8, -1000, 2).

    2. u(1), u(2), ..., u(N) : a sequence setting a number of elements which are being included into Black Box at the moment of first, second, ... and N-transaction GET. For the Example 1 we have u=(1, 2, 6, 6).

    The Black Box algorithm supposes that natural number sequence u(1), u(2), ..., u (N) is sorted in non-descending order, N<=M and for each p (1<=p<=N) an inequality p<=u(p)<=M is valid. It follows from the fact that for the p-element of our u sequence we perform a GET transaction giving p- minimum number from our A(1),A(2),...,A(u(p)) sequence.

    Input data

    Input starts with a positive integer equal to number of data sets. Each data set contains (in given order): M, N, A(1), A(2), ..., A(M), u(1), u(2), ..., u(N). All numbers are divided by spaces and (or) end-of-line characters.

    Input example: 

    2
1 1
1
1
7 4
3 1 -4 2 8 -1000 2
1 2 6 6

    Output data

    Write to the output Black Box answers sequence for each data set. All the numbers should be written in separate lines.

    Our example gives: 

    1
3
3
1
2