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 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
gopal252:
2023-09-06 13:00:43
since every subarray is a subset and also it's given that n>=c, so there will always be at least one subarray where (subarray sum)%c = 0, so we just need to find the first such subarray |
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hv22:
2023-01-25 23:12:50
solved in one go using your mom |
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smso:
2023-01-03 09:15:11
subarray answer always exist but subset is also possible, that's a bit confusing Last edit: 2023-09-09 16:53:41 |
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yash9274:
2021-09-24 20:51:42
ALERT:
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akshatjain_258:
2020-06-22 06:53:39
It is simply Pigeonhole Principle Last edit: 2020-06-22 06:55:02 |
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Dipankar Niranjan:
2018-05-10 15:52:53
Beautiful problem. |
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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. |
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i_am_looser:
2015-06-12 10:44:29
I found solution from internet which doesn't print "no sweets" but got ac... why?
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Ashish Sareen:
2015-03-19 10:52:32
nice problem :D
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parbays:
2014-01-21 17:08:31
its outputting the neighbours indices not values. Got one WA to realise that. |
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 |