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 Answer 


      (elements are arranged by non-descending)



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 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, 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.