HALLOW  Halloween treats
Every year there is the same problem at Halloween: Each neighbor is only willing to give a certain total number of sweets on that day, no matter how many children call on him, so it may happen that a child will get nothing if it is too late. To avoid conflicts, the children have decided they will put all sweets together and then divide them evenly among themselves. From last year's experience of Halloween they know how many sweets they get from each neighbour. Since they care more about justice than about the number of sweets they get, they want to select a subset of the neighbours to visit, so that in sharing every child receives the same number of sweets. They will not be satisfied if they have any sweets left which cannot be divided.
Your job is to help the children and present a solution.
Input
The input contains several test cases.
The first line of each test case contains two integers c and n (1 ≤ c ≤ n ≤ 100000), the number of children and the number of neighbours, respectively. The next line contains n space separated integers a_{1} , ... , a_{n} (1 ≤ a_{i} ≤ 100000 ), where a_{i} represents the number of sweets the children get if they visit neighbour i.
The last test case is followed by two zeros.
Output
For each test case output one line with the indices of the neighbours the children should select (here, index i corresponds to neighbour i who gives a total number of a_{i} sweets). If there is no solution where each child gets at least one sweet, print "no sweets" instead. Note that if there are several solutions where each child gets at least one sweet, you may print any of them.
Example
Input: 4 5 1 2 3 7 5 3 6 7 11 2 5 13 17 0 0 Output: 3 5 2 3 4
hide comments
Dipankar Niranjan:
20180510 15:52:53
Beautiful problem. 

Agustin Santiago Gutierrez:
20150717 04:42:44
i_am_looser: Notice that your example test case is invalid, since c <= n must hold. This is very important. 

i_am_looser:
20150612 10:44:29
I found solution from internet which doesn't print "no sweets" but got ac... why?


Ashish Sareen:
20150319 10:52:32
nice problem :D


parbays:
20140121 17:08:31
its outputting the neighbours indices not values. Got one WA to realise that. 

Abhishek Kumar:
20130521 19:52:47


Rajarshi Sarkar:
20130429 17:15:27
15s ? 

BLANKRK:
20120819 18:32:31
nice one!!! 

Rajkiran Rajkumar:
20120414 01:46:20
For the first example test case,


:D:
20110113 14:04:39
yes 
Added by:  Simon 
Date:  20070705 
Time limit:  2.235s 
Source limit:  50000B 
Memory limit:  1536MB 
Cluster:  Cube (Intel G860) 
Languages:  All except: ERL GOSU JSRHINO NODEJS PERL6 VB.NET 
Resource:  University of Ulm Local Contest 2007/2008 