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 <cstdio>
#include <cmath>
#include <iostream>
#include <sstream>
#include <string>
#include <vector>
#include <map>
#include <queue>
#include <algorithm>

#ifdef _DEBUG
#define DMP(x) cerr << #x << ": " << x << "\n"
#else
#define DMP(x) ((void)0)
#endif

const int MOD = 1000000007, INF = 1111111111; 
using namespace std;
using lint = long long;

int main() {

	cin.tie(nullptr);
	ios::sync_with_stdio(false);

	int N, K;
	cin >> N >> K;

	int combi = (N - 1) * (N - 2) / 2;
	if (K > combi) {
		cout << "-1" << "\n";
	}
	else if( N!=2 ){
		for (int i = 2; i <= N; i++) {
			cout << 1 << " " << i << "\n";
		}
		int cnt = 2;
		bool flag = true;
		while(flag){
			for (int i = cnt + 1; i <= N; i++) {
				if (combi - K == 0) {
					flag = false;
					break;
				}
				cout << cnt << " " << i << "\n";
				K++;
			}
			cnt++;
		}
	}

	return 0;
}