Odd-Degree Graph

Given two integers $N,K$, construct an undirected graph satisfying all of the following conditions.

• It has $N$ vertices, numbered from $1$ to $N$.
• It has no self-loops or multiple edges between the same pair of vertices.
• A path exists between every pair of vertices.
• Exactly $K$ vertices have odd degree.
• It has at most $2N$ edges.

The degree of a vertex is the number of edges incident to it. If no such graph exists, print -1.

The input is given in the following format:

$T$ $\mathrm{case}_1$ $\mathrm{case}_2$

For each test case, if no valid graph exists, print -1 on a single line.

Otherwise, first print the number of edges $M$ ($0 \leq M \leq 2N$). On each of the next $M$ lines, print the endpoints $u_i,v_i$ of an edge (), separated by a space.

• $1 \leq T \leq 100\,000$.
• $1 \leq K \leq N \leq 100\,000$.