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>
#include<iomanip>
using namespace std;
#define rep(i,n) for(int i=0;i<n;i++)
typedef long long ll;
typedef long  l;
typedef pair<int,int> P;
const int INF=100100100;
const double PI=3.141592653589;


int main(){
  int n,k; cin>>n>>k;
  bool ans=0;
  if((n-1)*(n-2)/2<k)
  ans=1;

  vector<P> p;
  if(ans)
  cout<<-1<<endl;
  else{
    for(int i=1;i<n;i++){
      p.push_back({1,i+1});
    }
    // k=(n-1)*(n-2)/2-x
    vector<P> ad;
    for(int i=2;i<=n;i++){
      for(int j=i+1;j<=n;j++){
        ad.push_back({i,j});
      }
    }
    rep(i,(n-1)*(n-2)/2-k){
      p.push_back(ad[i]);
    }
    cout<<p.size()<<endl;
    rep(i,p.size()){
      cout<<p[i].first<<" "<<p[i].second<<endl;
    }

  }

  return 0;
}