Friendships

AtCoder

IDabc131_e

Time2000ms

Memory256MB

Difficulty—

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. * $2 \leq N \leq 100$ * $0 \leq K \leq \frac{N(N - 1)}{2}$ ## Input Input is given from Standard Input in the following format: $N$ $K$ [samples]

Samples

Input #1

5 3

Output #1

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.

Input #2

5 8

Output #2

\-1

There is no graph satisfying the conditions.

API Response (JSON)

{
  "problem": {
    "name": "Friendships",
    "description": {
      "content": "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 num",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc131_e"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "Does there exist an undirected graph with $N$ vertices satisfying the following conditions?\n\n*   The graph is simple and connected.\n*   The vertices are numbered $1, 2, ..., N$.\n*   Let $M$ be the num...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments