24688번 - Diameter Two 스페셜 저지다국어

You are building a computer network for a new company. The network consists of $n$ nodes numbered from $1$ to $n$. The nodes can be connected via bidirectional wires. Each wire connects exactly two nodes. Each pair of nodes can be connected with at most one wire. If a wire connects two nodes, we'll say that these two nodes are directly connected.

The first $k$ nodes (with indices $1, 2, \ldots, k$) will be untrusted and must be connected to the network securely. Each of these nodes must be directly connected to exactly one other node.

The remaining $n-k$ nodes (with indices $k+1, k+2, \ldots, n$) will be trusted and must be connected to the network reliably. Each of these nodes must be directly connected to at least two other nodes.

The diameter of the network must not exceed $2$: for any two nodes $i$ and $j$, they must either be directly connected, or there must exist a node $k$ such that nodes $i$ and $k$ are directly connected, and nodes $k$ and $j$ are directly connected.

To minimize the costs, the number of used wires must be as small as possible.

Build a network satisfying all the conditions above, or report if this is impossible.

Each test contains multiple test cases. The first line contains the number of test cases $t$ ($1 \le t \le 50$). Description of the test cases follows.

The only line of each test case contains two integers $n$ and $k$, denoting the total number of nodes and the number of untrusted nodes, respectively ($3 \le n \le 50$; $0 \le k \le n$).

For each test case, if it is impossible to build a network satisfying the given conditions, print a single integer $-1$.

Otherwise, in the first line, print the number of used wires $m$. In each of the following $m$ lines, print two integers $u_i$ and $v_i$, denoting the indices of the nodes connected with the $i$-th wire ($1 \le u_i, v_i \le n$; $u_i \ne v_i$).