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;
  if(K>(N-1)*(N-2)/2){
    cout << -1 << endl;
  }
  else{
    cout << N-1+(N-1)*(N-2)/2-K << endl;
    for(int i=2; i<=N; i++){
      cout << 1 << ' ' << i << endl;
    }
    int i=2;
    for(; N-i<(N-1)*(N-2)/2-K; i++){
      for(int j=0; j<N-i; j++){
        cout << i << ' ' << i+1+j << endl;
      }
      K+=N-i;
    }
    for(int j=0; j<(N-1)*(N-2)/2-K; j++){
      cout << i << ' ' << i+1+j << endl;
    }
  }
}