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: Accepted)

#include <bits/stdc++.h>
using namespace std;

#define INF (INT32_MAX/2)

int main() {
	int N, K;

	cin >> N >> K;

	int ma = (N - 1) * (N - 2) / 2;
	if( K > ma ) {
		cout << -1 << endl;
	}
	else {
		int num = ma - K;
		cout << N - 1 + num << endl;
		for( int i = 2; i <= N; i++ ) {
			cout << 1 << " " << i << endl;
		}
		int n = 0;
		int flag = 0;
		for( int i = 2; i <= N - 1; i++ ) {
			for( int j = i + 1; j <= N ; j++ ) {
				if( n >= num ) {
					flag = 1;
					break;
				}
				cout << i << " " << j << endl;
				n++;
			}
			if( flag ) {
				break;
			}
		}
	}
}