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## Page 1
10190
Divide, But Not Quite Conquer!
Your goal in this problem is to divide a certain integer n by another integer m until n = 1, obtaining
a sequence of numbers. Lets call a[i] each number of this sequence, and let’s say it has k numbers (i.e.
you must do k −1 succesive divisions to reach n = 1). You can only have this sequence if the following
restrictions are met:
• a[1] = n, a[i] = a[i −1] ÷ m, for all 1 < i ≤k
• a[i] is divisible by m (that is, a[i] mod m = 0) for all 1 ≤i < k
• a[1] > a[2] > a[3] > . . . > a[k]
For instance, if n = 125 and m = 5, you have 125, 25, 5 and 1 (you did 3 divisions: 125/5, 25/5 and
5/5). So, k = 4, a[1] = 125, a[2] = 25, a[3] = 5 and a[4] = 1.
If n = 30 and m = 3, you have 30, 10, 3 and 1. But a[2] = 10, and 10 mod 3 = 1, so there is no
sequence because it violates restriction 2. When the sequence doesn’t exist we think it’s not fun and,
thus, very boring!
Input
The input will consist on an arbitrary number of lines.
Each line will consist of two non-negative
integers n, m which are both less than 2000000000. You must read until you reach the end of file.
Output
For each pair n, m you must print the correspondent sequence a (as defined above) in a single line, with
each adjacent numbers of the sequence separated by a single space. In the case the sequence doesn’t
exist because it violates some restriction, just print the phrase ‘Boring!’ in a single line (without the
quotes).
Sample Input
125 5
30 3
80 2
81 3
Sample Output
125 25 5 1
Boring!
Boring!
81 27 9 3 1 |