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 on a piece of paper, consisting of a permutation of positive integers from to . Then, he wrote down an array of length on the paper. The array is constructed by taking the Greatest Common Divisor (GCD) of each element and the corresponding element . Namely, . However, he ~~purposely~~ accidentally lost the paper and cannot remember what the arrays and were. Fortunately, he still remembers that there are exactly unique integers in array . Can you please help him find a possible array ?

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

#### Input Specification

The first line of input contains two integers and .

The following table shows how the available marks are distributed.

Marks Awarded | ||
---|---|---|

marks | ||

marks |

#### Output Specification

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

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

#### Sample Input

`5 3`

#### Sample Output

`5 4 3 2 1`

#### Explanation for Sample

The array for sample output is which is . In array , there are exactly unique integers: , , and .

## Comments