Once upon a time, in a quaint village surrounded by lush forests, there lived a toucan named Owen, who was also a mathematician. Owen, being quite the playful bird, wrote down an array $a$ on a piece of paper, consisting of a permutation of positive integers from $1$ to $N$. Then, he wrote down an array $b$ of length $N$ on the paper. The array $b$ is constructed by taking the Greatest Common Divisor (GCD) of each element $a_i$ and the corresponding element $a_{a_i}$. Namely, $b_i=gcd(a_i,a_{a_i})$. However, he purposely accidentally lost the paper and cannot remember what the arrays $a$ and $b$ were. Fortunately, he still remembers that there are exactly $K$ unique integers in array $b$. Can you please help him find a possible array $a$?

Note: A permutation of length $n$ is an array consisting of $n$ distinct integers from $1$ to $n$ in any order.

Input Specification

The first line of input contains two integers $N$ and $K$.

The following table shows how the available $15$ marks are distributed.

Marks Awarded	$N$	$K$
$3$ marks	$1\le N\le {10}^6$	$K\in \{1,N\}$
$12$ marks	$1\le N\le {10}^6$	$1\le K\le N$

Output Specification

Output a possible array $a$, a permutation of positive integers from $1$ to $N$.

It can be proven that there is always a valid array $a$.

Sample Input

5 3

Sample Output

5 4 3 2 1

Explanation for Sample

The array $b$ for sample output is $[gcd(a_1,a_5),gcd(a_2,a_4),gcd(a_3,a_3),gcd(a_4,a_2),gcd(a_5,a_1)]$ which is $[1,2,3,2,1]$. In array $b$, there are exactly $3$ unique integers: $1$, $2$, and $3$.