Generalized Arithmetic Progression Free Sequence

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For given two positive integers a and b let's construct the sequence x[1], x[2], ... by the following rules. For k=1 we put x[1]=1. Now let k >= 2. Then x[k] is the least positive integer such that the following two conditions hold
 x[k] > x[k  1];
 for all i, j < k we have x[k] is not equal to a * x[i]  b * x[j].
You need to find the first n terms of this sequence.
Remark. Let a=2 and b=1. Then we see that sequence x[1], x[2], ... does not contain any arithmetic progression of length three as its subsequence. This justifies the problem title.
Input
The first line contains a single integer T, the number of test cases. T test cases follow. The only line of each test case contains three integers a, b and n.
Output
For each test case, output a single line containing the numbers x[1], x[2], ..., x[n] generated by the rules given in the problem statement and numbers a, b. Separate any two consecutive numbers in a line by a single space.
Constraints
1 <= T <= 50
1 <= a, b <= 50
1 <= n <= 1000
Example
Input: 3 2 1 10 1 1 5 4 2 4 Output: 1 2 4 5 10 11 13 14 28 29 1 2 3 4 5 1 3 4 5
Author:  anton_lunyov 
Tags  anton_lunyov, cook15, easy 
Date Added:  5102011 
Time Limit:  0.712667 sec 
Source Limit:  50000 Bytes 
Languages:  C, CPP14, JAVA, PYTH, PYTH 3.6, CS2, PAS fpc, PAS gpc, RUBY, PHP, GO, NODEJS, HASK, SCALA, D, PERL, FORT, WSPC, ADA, CAML, ICK, BF, ASM, CLPS, PRLG, ICON, SCM qobi, PIKE, ST, NICE, LUA, BASH, NEM, LISP sbcl, LISP clisp, SCM guile, JS, ERL, TCL, PERL6, TEXT, CLOJ, FS 
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