Fatigued by the endless toils of farming, Farmer John has decided
to try his hand in the MP3 player market with the new iCow. It is
an MP3 player that stores N songs (1 <= N <= 1,000) indexed 1 through
N that plays songs in a "shuffled" order, as determined by Farmer
John's own algorithm:
* Each song i has an initial rating R_i (1 <= R_i <= 10,000).
* The next song to be played is always the one with
the highest rating (or, if two or more are tied, the highest
rated song with the lowest index is chosen).
* After being played, a song's rating is set to zero, and its rating
points are distributed evenly among the other N-1 songs.
* If the rating points cannot be distributed evenly (i.e.,
they are not divisible by N-1), then the extra points are
parceled out one at a time to the first songs on the list
(i.e., R_1, R_2, etc. -- but not the played song) until no
more extra points remain.
This process is repeated with the new ratings after the next song
is played.
Determine the first T songs (1 <= T <= 1000) that are played by the
iCow.
Input
* Line 1: Two space-separated integers: N and T
* Lines 2..N+1: Line i+1 contains a single integer: R_i
Output
* Lines 1..T: Line i contains a single integer that is the i-th song
that the iCow plays.