| ## 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 |