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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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