Canadian Computing Competition: 2014 Stage 1, Junior #4, Senior #1
You are hosting a party and do not have room to invite all of your friends. You use the following unemotional mathematical method to determine which friends to invite.
Number your friends 
~1, 2, \dots, K~ and place them in a list in this order. Then perform 
~m~ rounds. In each round, use a number to determine which friends to remove from the ordered list.
The rounds will use numbers 
~r_1, r_2, \dots, r_m~. In round 
~i~ remove all the remaining people in positions that are multiples of 
~r_i~ (that is, 
~r_i, 2r_i, 3r_i, \dots~) The beginning of the list is position 
~1~.
Output the numbers of the friends that remain after this removal process.
Input Specification
The first line of input contains the integer 
~K~ 
~(1 \le K \le 100)~. The second line of input contains the integer ~m~ 
~(1 \le m \le 10)~, which is the number of rounds of removal. The next ~m~ lines each contain one integer. The 
~i^{th}~ of these lines 
~(1 \le i \le m)~ contains ~r_i~ 
~(2 \le r_i \le 100)~ indicating that every person at a position which is multiple of ~r_i~ should be removed.
Output Specification
The output is the integers assigned to friends who were not removed. One integer is printed per line in increasing sorted order.
Sample Input
10
2
2
3
Output for Sample Input
1
3
7
9
Explanation of Output for Sample Input
Initially, our list of invitees is 
~1, 2, 3, 4, 5, 6, 7, 8, 9, 10~. There will be two rounds of removals. After the first round of removals, we remove the even positions (i.e., every second position), which causes our list of invitees to be 
~1, 3, 5, 7, 9~. After the second round of removals, we remove every 3rd remaining invitee: thus, we keep ~1~ and 
~3~, remove 
~5~ and keep 
~7~ and 
~9~, which leaves us with an invitee list of 
~1, 3, 7, 9~.
Comments
this took me way longer than expected
hardest Junior 4 in a while
agreed
is this sarcasm or something
buddy this is senior 1
Canadian Computing Competition: 2014 Stage 1, Junior #4, Senior #1
So... actually thunder200911133 isn't wrong. it is both J4 and S1.
holy nerd emoji
fax