HALLOW - Halloween treats

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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 a1 , ... , an (1 ≤ ai ≤ 100000 ), where ai 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 ai 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: 2018-05-10 15:52:53

Beautiful problem.

Agustin Santiago Gutierrez: 2015-07-17 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: 2015-06-12 10:44:29

I found solution from internet which doesn't print "no sweets" but got ac... why?
and also for test case
4 3
1 2 3
0 0
prints nothing.

Ashish Sareen: 2015-03-19 10:52:32

nice problem :D
only coding style is gonna save you... same methodology can bring you TLE or top ten(10) ranking based on how you code

Last edit: 2015-03-19 11:03:54
parbays: 2014-01-21 17:08:31

its outputting the neighbours indices not values. Got one WA to realise that.

Abhishek Kumar: 2013-05-21 19:52:47


Last edit: 2013-05-22 17:26:40
Rajarshi Sarkar: 2013-04-29 17:15:27

15s ?

BLANKRK: 2012-08-19 18:32:31

nice one!!!

Rajkiran Rajkumar: 2012-04-14 01:46:20

For the first example test case,

1 3 4 5 is also a solution, correct?

:D: 2011-01-13 14:04:39

yes


Added by:Simon
Date:2007-07-05
Time limit:2.235s
Source limit:50000B
Memory limit:1536MB
Cluster: Cube (Intel G860)
Languages:All except: ERL GOSU JS-RHINO NODEJS PERL6 VB.NET
Resource:University of Ulm Local Contest 2007/2008