Problem:
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}

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.

Sample Input 1

5 3

Sample 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.

Sample Input 2

5 8

Sample Output 2

-1

There is no graph satisfying the conditions.

Solution in C++14 (GCC 5.4.1) (judge verdict: Accepted)

#include <bits/stdc++.h>
using namespace std;

int main() {
  int N, K; cin >> N >> K;
  int max_p = (N-1) * (N-2) / 2;  // 距離 2 の組数の上限
  if (max_p < K) { cout << -1 << endl; return 0; }
  vector<pair<int, int>> ans;
  // うにを作ると距離 2 の組は max_p 組できる
  for (int i = 0; i < N-1; i++) {
    ans.push_back(make_pair(i+1, N));
  }
  // うにの先端の頂点同士を結ぶと、距離 2 の組が 1 つ減る
  int add = max_p - K;
  vector<pair<int, int>> E;  // 加える辺の候補を挙げておく
  for (int i = 0; i < N-2; i++) {
    for (int j = i+1; j < N-1; j++) {
      E.push_back(make_pair(i+1, j+1));
    }
  }
  for (int i = 0; i < add; i++) ans.push_back(E.at(i));
  cout << ans.size() << endl;
  for (int i = 0; i < ans.size(); i++) {
    cout << ans.at(i).first << " " << ans.at(i).second << endl;
  }
}