Problem Statement

We have an undirected graph with N vertices numbered 0 through N-1 and no edges at first.
You may add edges to this graph as you like.
When you are done with adding edges, the following operation will be performed once using a given integer K.

• For each edge you have added, let u and v be its endpoints, and an edge will be added between two vertices $(u+K) \mathrm{mod} N$ and $(v+K) \mathrm{mod} N$.
  This edge will be added even if there is already an edge between these vertices, resulting in multi-edges.

For the given N and K, find a set of edges that you should add so that the graph will be a tree after the operation.
If there is no such set of edges, indicate that fact.

Input

The input is given from Standard Input in the following format:
N K

Output

If there is a set of edges that satisfies the requirement, let M be the number of edges, and a_i and b_i be the two vertices connected by the i-th edge, and print a solution in the following format.
Here, $0\leq M\leq N$ must hold, and all values must be integers. The edges may be printed in any order, as well as the endpoints of an edge.
M
a_1 b_1
a_2 b_2
$\vdots$
a_M b_M

If multiple solutions exist, any of them will be accepted.
If no set of edges satisfies the requirement, print -1.

Constraints

• $2\leq N\leq 2\times 10^5$
• $1\leq K\leq N-1$
• All values in the input are integers.

Sample Input 1

5 2

Sample Output 1

2
2 3
2 4

The operation will add the edges 4-0 and 4-1.
Then, the graph will be a tree, so this is a legitimate output.

Sample Input 2

2 1

Sample Output 2

-1

There is no way to have a tree after the operation.

Sample Input 3

7 1

Sample Output 3

3
0 1
2 3
4 5

见题面 Input 部分

见题面 Output 部分