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 rep(i, a, n) for (int i = a, _n = n; i <= _n; ++i)
#define drep(i, a, n) for (int i = a, _n = n; i >= n; --i)
#define debug(x) cout << #x <<" = "<< x << endl

int n, k;

int main () {
	scanf ("%d%d", &n, &k);
	if (k > (n - 2) * (n - 1) / 2) {
		puts("-1");
		return 0;
	}

	int t = (n - 2) * (n - 1) / 2, m = n - 1;

	while (t > k) --t, ++m;

	printf ("%d\n", m);

	rep(i, 2, n) printf ("%d %d\n", 1, i);

	m -= n - 1;	

	rep(i, 2, n) rep(j, i + 1, n) {
		if (m == 0) return 0;
		--m;
		printf ("%d %d\n", i, j);
	}

	return 0;
}