Problem 1030 - USTC Online Judge

Rank

Problem 1030

Black Box

Time Limit: 1000ms
Memory Limit: 65536kb

Description

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, 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

nput 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. There maybe several cases.

Output

Write to the output Black Box answers sequence for a given sequence of transactions. The numbers must be separated with end-of-line characters.You must seperate all the sequences by a single empty line.

Sample Input

7 4
3 1 -4 2 8 -1000 2
1 2 6 6

Sample Output

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