Competitions

# 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.

Consider the Example:

 N Transaction i Black Box contents after transaction 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, m30000. For the Example 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 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 (1pn) 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

The input dataset contains numbers: 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.

Output

Print the Black Box answers sequence for a given sequence of transactions. Each number must be printed in the separate line.

Time limit 1 second
Memory limit 64 MiB
Input example #1
7 4
3 1 -4 2 8 -1000 2
1 2 6 6

Output example #1
3
3
1
2