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<string>
#include<queue>
#include<algorithm>
#include<map>
#include<set>
#include<vector>
#include<math.h>

using namespace std;

#define INF 1000000007
#define LINF (1LL << 62)

typedef long long i64;
typedef pair<i64,i64> P;


int n, k;

int main(){
	cin >> n >> k;
	
	if(k > (n-1)*(n-2)/2){
		cout << -1 << endl;
		return 0;
	}
	//1,2 1,3 1,4 1,5 2,3 2,4 2,5 3,4 3,5 4,5
	vector<P> ans;
	for(int j = 2; j <= n; j++){
		ans.push_back(P(1,j));
	}
	k -= (n-1)*(n-2)/2;
	for(int i = 2; i < n; i++){
		for(int j = i+1; j <= n; j++){
			ans.push_back(P(i,j));
			k++;
			if(k == 0) break;
		}
		if(k == 0) break;
	}
	
	cout << ans.size() << endl;
	for(int i = 0; i < ans.size(); i++){
		cout << ans[i].first << " " << ans[i].second << endl;
	}
	
	return 0;
}