402051: GYM100633 I Accounting Numeral System
Description
The latest Accounting Numeral System is the top accounting system in the whole world. Its creator, Dr. Ceizenpok, is the best expert of the respective authority. Any positive integer n in this system based m is represented as a sum of m parts:
while x1, x2, ... , xm — are such integers that 0 ≤ x1 < x2 < ... < xm. Numbers our experts call accounting indexes. Each number n in this system is recorded as , and it is considered that 0! = 1 and Ckm = 0, if m > k. For example, number 9 in the accounting system based 3 is recorded as (4)(3)(2), because , and number 1 in this system based 2 looks like:(2)(0), because .
You have to find a representation of an integer n in the accounting numeral system based m.
InputSingle line contains two integers n and m (1 ≤ n ≤ 1016, 2 ≤ m ≤ 1 000).
OutputSingle line should contain a sequence of m space-separated integers xm, ..., x2, x1, that form a number designation n in the accounting numeral system. Number xm is the leftmost digit in the number designation n, and x1 — its rightmost one.
ExamplesInput9 3Output
4 3 2Input
5 2Output
3 2