E - Friendships

Score: $500$ points

Problem Statement

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.

Constraints

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

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Input

Input is given from Standard Input in the following format:

$N$ $K$

Output

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.

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5 3

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.

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5 8

-1

There is no graph satisfying the conditions.