Accounting Numeral System

The Accounting Numeral System is the top accounting system in the whole world. Its creator, Dr. Ceizenpok, is the leading expert of the respective authority.

In the accounting numeral system with base $m$, a positive integer $n$ is written as a sum of $m$ parts:

$n = C_{x_m}^m + C_{x_{m-1}}^{m-1} + C_{x_{m-2}}^{m-2} + \cdots + C_{x_1}^1$

Here $x_1, x_2, \ldots, x_m$ are integers with $0 \le x_1 < x_2 < \cdots < x_m$. The numbers $C_k^m = \frac{k!}{m!\,(k-m)!}$ are called accounting indexes. Here $0! = 1$, and $C_k^m = 0$ if $m > k$.

The number $n$ is written as $\overline{(x_m) \ldots (x_2)(x_1)}$. For example, 9 in base 3 is written as (4)(3)(2), because $9 = C_4^3 + C_3^2 + C_2^1$. The number 1 in base 2 is written as (2)(0), because $1 = C_2^2 + C_0^1$.

Find the representation of the integer $n$ in the accounting numeral system with base $m$.

The only line contains two integers $n$ and $m$ ($1 \le n \le 10^{16}$, $2 \le m \le 1\,000$).

Print one line with $m$ space-separated integers $x_m, \ldots, x_2, x_1$ that form the representation of $n$ in the accounting numeral system. $x_m$ is the leftmost number of the representation, and $x_1$ is the rightmost.