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;

#define ll long long

int solve(int n){
	int t=n-1;
	t*=n-2;
	t/=2;
	return t;
}

int main(){
	ios_base::sync_with_stdio(false);
	cin.tie(0);cout.tie(0);

	int n,k,t,flag=1;
	vector<pair<int,int>> edges;
	cin>>n>>k;
	int v=1;
	t=solve(n);
	if(k>t) flag=0;
	for(int i=n;i>1;i--){
		t=solve(i);
		if(k>=t){
			for(int j=1;j<i;j++){
				edges.push_back({v,v+j});
			}
			v+=i;
			i=min(i,n-v+2);
			k-=t;
			if(k==0) break;
		}
	}
	if(k>0){

	}
	if(k>0) flag=0;
	if(flag){
		cout<<edges.size()<<"\n";
		for(int i=0;i<edges.size();i++){
			cout<<edges[i].first<<" "<<edges[i].second<<"\n";
		}
	}
	else cout<<"-1\n";

	return 0;
}