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 \leq N \leq 10^6~	~K \in \{1, N\}~
~12~ marks	~1 \leq N \leq 10^6~	~1 \leq K \leq 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~.