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;
typedef long long ll;
typedef pair<int,int> pii;
#define pb push_back
#define mp make_pair
#define rep(i,n) for(int i=0;i<(n);++i)
constexpr int mod=1000000007;
constexpr int mod1=998244353;
vector<int> dx={0,-1,0,1},dy={1,0,-1,0};
bool inside(int y,int x,int h,int w){
	if(y<h && y>=0 && x<w && x>=0) return true;
	return false;
}



int main(){
	cin.tie(0);
	ios::sync_with_stdio(false);
	int n,k;cin >> n >> k;
	int m=n*(n-1)/2;
	if(k<n-2 || (k>n-2 && k<n+1)) cout << -1 << endl;
	else if(k==n-2){
		cout << n-1 << endl;
		rep(i,n-1) cout << i+1 << " " << i+2 << endl;
	}
	else if(k==m){
		cout << m << endl;
		for(int i=1;i<=n;++i){
			for(int j=i+1;j<=n;++j){
				cout << i << " " << j << endl;
			}
		}
	}
	else{
		vector<pii> ans;
		int cnt=n+1;
		rep(i,n-1){
			ans.pb(mp(i+1,i+2));
		}
		ans.pb(mp(1,3));
		int i=1,j=4;
		while(cnt<k){
			ans.pb(mp(i,j));
			cnt++;
			if(i+3==j) i++;
			else{
				if(j==n) break;
				j++;
			}
		}
		if(cnt==k){
			cout << ans.size() << endl;
			rep(i,ans.size()){
				cout << ans.at(i).first << " " << ans.at(i).second << endl;
			}
		}
		else cout << -1 << endl;
	}
}