Problem J
                                          Stacking Cups
                                        Time limit: 2 seconds
You have a collection of n cylindrical cups, where the ith cup is 2i − 1 cm tall. The cups have increasing
diameters, such that cup i fits inside cup j if and only if i < j. The base of each cup is 1 cm thick (which
makes the smallest cup rather useless as it is only 1 cm tall, but you keep it for sentimental reasons).
After washing all the cups, you stack them in a tower. Each cup is placed upright (in other words, with
the opening at the top) and with the centers of all the cups aligned vertically. The height of the tower is
defined as the vertical distance from the lowest point on any of the cups to the highest. You would like
to know in what order to place the cups such that the final height (in cm) is your favorite number. Note
that all n cups must be used.
For example, suppose n = 4 and your favorite number is 9. If you place the cups of heights 7, 3, 5, 1, in
that order, the tower will have a total height of 9, as shown in Figure J.1.

                                    9
                                    8
                                    7
                                    6
                                    5
                                    4
                                    3
                                    2
                                    1
                                    0

                               Figure J.1: Illustration of Sample Output 1.

Input

The input consists of a single line containing two integers n and h, where n (1 ≤ n ≤ 2 · 105 ) is the
number of cups and h (1 ≤ h ≤ 4 · 1010 ) is your favorite number.

Output

If it is possible to build a tower with height h, output the heights of all the cups in the order they should
be placed to achieve this. Otherwise, output impossible. If there is more than one valid ordering of
cups, any one will be accepted.

49th ICPC World Championship Problem J: Stacking Cups © ICPC Foundation                                   19

Sample Input 1                                Sample Output 1
4 9                                           7 3 5 1

Sample Input 2                                Sample Output 2
4 100                                         impossible

49th ICPC World Championship Problem J: Stacking Cups © ICPC Foundation   20