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: Wrong Answer)

#include <bits/stdc++.h>
using namespace std;
int main(){
  int n,k,m;
  cin >> n >> k;
  if(k > (n*(n-3))/2 + 1)cout << -1 << endl;
  else{
    int num;
    int path[n+1][n+1];
    for(int i = 1;i <= n;i++){
      for(int j = i+1;j <= n;j++){
        path[i][j] = 1;
      }
    }
    int l = 0;
    for(int i = 1;i <= n;i++){
      for(int j = i+2;j <= n;j++){
        if(l >= k)break;
        path[i][j] = 0;
        l++;
      }
      if(l >= k)break;
    }
    m = (n*(n-3))/2 + n - k;
    cout << m << endl;
    for(int i = 1;i <= n;i++){
      for(int j = i+1;j <= n;j++){
        if(path[i][j] == 1)cout << i << " " << j << endl;
      }
    }
  }
}