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 Ruby (2.3.3) (judge verdict: Wrong Answer)

N,K=gets.chomp.split(' ').map{|n| n.to_i}
if(N==2)
	puts -1
	exit(0)
end
max = (N-1)*(N-2)/2
if(max < K)
	puts -1
	exit(0)
end
M = N-1+(max-K)
puts M
for i in 1..(N-1)
	puts "#{1} #{1+i}"
end
cnt = 0
for i in 2..(N-1)
	for j in 3..(N)
		if(cnt == max-K)
			exit(0)
		end
		puts "#{i} #{j}"
		cnt += 1
	end
end