All Tracks Math Number Theory Basic Number Theory-2 Problem

Mike and GCD Issues

Ad-Hoc, Greatest common divisor, Greatest common divisor, Mathematics, Number theory, gcd


Mike claims to be good at math, and a person having a photographic memory. Harvey does trust Mike, but he is not completely sure about these claims said by him. So, for reassurance, he gives the following task to Mike :

Given a 1-indexed array A of size N, the distance between any 2 indices of this array i and j is given by \(|i-j|\). Now, given this information, Mike needs to find for every index i (\( 1 \le i \le N)\), an index j, such that \(1 \le j \le N\), \(i \ne j\), and \(GCD(A[i],A[j]) > 1 \)

If there are multiple such candidates for an index i, you need to find and print the index j, such that the distance between i and j is minimal. If there still exist multiple candidates, print the minimum j satisfying the above constraints.

For each index i of this array, find and print an index j satisfying the conditions above. If, for any index i there does not exist any j, print 1 instead of its answer.

Input Format:

The first line contains a single integer N denoting the size of array A. The next line contains N space separated inetegers, where the \(i^{th}\) integer denotes \(A[i]\).

Output Format :

Print N space separated integers, where the \(i^{th}\) integer denotes an index j, where \(1 \le j \le N\), \(i \ne j\), and GCD\((A[i],A[j])>1\), and the distance between i and j is minimal if there exist multiple candidates satisfying the above constraints. If there still exist multiple candidates satisfying the above constraints, print the minimum j doing so.

Constraints :

\( 1 \le N \le 2 \times 10^5\)

\( 1 \le A[i] \le 2\times10^5 \)

2 3 4 9 17
3 4 1 2 -1

The closest index to index 1 satisfying the above constraints is index 3, as GCD(2,4)=2, that is greater than one. Similarily, the closest indices to indices \(2,3,\) and 4 are indices \(4,1\) and 2 respectively.

Time Limit: 1,0 sec(s) for each input file.
Memory Limit: 256 MB
Source Limit: 1024 KB

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