Does there exist an undirected graph with $N$ vertices satisfying the following conditions?

-   The graph is simple and connected.
-   The vertices are numbered $1, 2, ..., N$.
-   Let $M$ be the number of edges in the graph. The edges are numbered $1, 2, ..., M$, the length of each edge is $1$, and Edge $i$ connects Vertex $u_i$ and Vertex $v_i$.
-   There are exactly $K$ pairs of vertices $(i,\ j)\ (i < j)$ such that the shortest distance between them is $2$.

If there exists such a graph, construct an example.

Input is given from Standard Input in the following format:

```
$N$ $K$
```

If there does not exist an undirected graph with $N$ vertices satisfying the conditions, print `-1`.

If there exists such a graph, print an example in the following format (refer to Problem Statement for what the symbols stand for):

```
$M$
$u_1$ $v_1$
$:$
$u_M$ $v_M$
```

If there exist multiple graphs satisfying the conditions, any of them will be accepted.

-   All values in input are integers.
-   $2 \leq N \leq 100$
-   $0 \leq K \leq \frac{N(N - 1)}{2}$

5
4 3
1 2
3 1
4 5
2 3

This graph has three pairs of vertices such that the shortest distance between them is 2: (1, 4), (2, 4), and (3, 5). Thus, the condition is satisfied.

-1

There is no graph satisfying the conditions.