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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:
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