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).
本站邊界規則補充
本題在本站要求至少進行一次除法，亦即序列至少有兩項（k ≥ 2）。當 n ≤ 1 或 m ≤ 1 時，輸出 Boring!。這是針對原題未明寫的零次除法情況所作的本站明確約定，與既有評測一致。輸入仍以 EOF 結束，0 0 也需要輸出一行 Boring!，不是終止符。
範例輸入 1
125 5 30 3 80 2 81 3
範例輸出 1
125 25 5 1 Boring! Boring! 81 27 9 3 1
Pro 專屬功能： 查看這題在歷屆 CPE 出現過幾次 — 升級以解鎖.