Booth Allocation by Garlic Association

T University hosts a large "Club Recruitment Fair" in which clubs are allocated a limited number of booths along a line with H slots. Given T clubs with contributions u_i (in submission order), the coordinator decides to allocate booths using the following process:

For each club, compute the sequence: \[ u_i, \frac{u_i}{2}, \frac{u_i}{2^2}, \cdots, \frac{u_i}{2^{H-1}}. \]

Then, across all T × H computed values, repeat the following until all H booths are allocated:

1. Remove one occurrence of the current maximum value and assign a booth to its corresponding club.
2. If there are multiple occurrences of the maximum value, apply these tie-breakers in order:
   1. If one or more clubs among the tied candidates have not yet received any booth, only consider those clubs.
   2. From the remaining clubs, choose the club with the largest original contribution \(u_i\).
   3. If there is still a tie, choose the club that submitted its application earlier (i.e. lower index).

Calculate and output how many booths each club receives.

inputFormat

The first line contains two integers T and H, where T is the number of clubs and H is the number of booths.

The second line contains T space-separated integers \(u_1, u_2, \ldots, u_T\) representing each club's contribution.

outputFormat

Output T integers separated by spaces, where the i-th integer is the number of booths allocated to the i-th club.

sample

3 5
118 100 80

2 2 1