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 <iostream>
#include <algorithm>
#include <string>
#include <vector>
#include <cmath>
#include <utility>
#include <iomanip>
using namespace std;
typedef long long ll;
typedef pair<int,int> P;
const ll MOD = 1e9+7;
vector<P> hen;

int main()
{
	int n,k;
	ll ans=0;
	cin>>n>>k;
	int mx=(n-2)*(n-1)/2;//最大数
	if(k>mx)
	{
		cout<<-1<<endl;
	}else{
		for(int i=1;i<n;i++)
			hen.push_back(P(i,n));
		//潰す個数だけ辺を張る
		int cnt=0;
		bool f=true;
		for(int i=1;i<n;i++)
		{
			for(int j=i+1;j<n;j++)
			{
				hen.push_back(P(i,j));
				cnt++;
				if(cnt==mx-k)
				{
					f=false;
					break;
				}
			}
			if(!f)
				break;
		}
		cout<<hen.size()<<endl;
		for(int i=0;i<hen.size();i++)
			cout<<hen[i].first<<" "<<hen[i].second<<endl;
	}
	return 0;
}