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2159.   Black Box
Time Limit: 1.0 Seconds   Memory Limit: 65536K
Total Runs: 662   Accepted Runs: 221    Multiple test files

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:

Example 1:

 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, NM and for each p (1 ≤ pN) an inequality pu(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 data 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) carriage return characters.

Input data, corresponding to Example 1:

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

Output data

Write to the standard output Black Box answers sequence for a given sequence of transactions. One number each line.

Our example gives:

3
3
1
2

• Source: Northeastern European 1996
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