A8960 | Secret

The Greatest Secret Ever consists of $n$ words, indexed by positive integers from $1$ to $n$ . The secret needs dividing between $k$ Keepers (let's index them by positive integers from $1$ to $k$ ), the $i$ -th Keeper gets a non-empty set of words with numbers from the set $U_{i}=(u_{i,1},u_{i,2},...,u_{i,|Ui}|)$ . Here and below we'll presuppose that the set elements are written in the increasing order.

We'll say that the secret is safe if the following conditions are hold:

- for any two indexes $i,j$ ( $1<=i<j<=k$ ) the intersection of sets $U_{i}$ and $U_{j}$ is an empty set;
- the union of sets $U_{1},U_{2},...,U_{k}$ is set $(1,2,...,n)$ ;
- in each set $U_{i}$ , its elements $u_{i,1},u_{i,2},...,u_{i,|Ui}|$ do not form an arithmetic progression (in particular, $|U_{i}|>=3$ should hold).

Let us remind you that the elements of set $(u_{1},u_{2},...,u_{s})$ form an arithmetic progression if there is such number $d$ , that for all $i$ ( $1<=i<s$ ) fulfills $u_{i}+d=u_{i+1}$ . For example, the elements of sets $(5)$ , $(1,10)$ and $(1,5,9)$ form arithmetic progressions and the elements of sets $(1,2,4)$ and $(3,6,8)$ don't.

Your task is to find any partition of the set of words into subsets $U_{1},U_{2},...,U_{k}$ so that the secret is safe. Otherwise indicate that there's no such partition.

The input consists of a single line which contains two integers $n$ and $k$ ( $2<=k<=n<=10^{6}$ ) — the number of words in the secret and the number of the Keepers. The numbers are separated by a single space.

If there is no way to keep the secret safe, print a single integer "-1" (without the quotes). Otherwise, print $n$ integers, the $i$ -th of them representing the number of the Keeper who's got the $i$ -th word of the secret.

If there are multiple solutions, print any of them.