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.split.map(&:to_i)

pairs_at_junction = [0, 1]

(2..n).each{|count|
    pairs_at_junction.push(count + pairs_at_junction.last)
}

define_method(:get_count_list){|sum, index|
    (1..index).reverse_each{|i|
        if pairs_at_junction[i] > sum
            next
        elsif pairs_at_junction[i] == sum
            return [pairs_at_junction[i]]
        else
            result = get_count_list(sum - pairs_at_junction[i], i)
            if result != nil
                return [pairs_at_junction[i]] + result
            end
        end
    }
    return nil
}

count_list = get_count_list(k, pairs_at_junction.size() - 1)
if count_list == nil || count_list.inject(:+) > n - 1
    puts -1
else
    current_num = 1
    next_num = 1
    count_list.each{|count|
        count.times{|cc|
            next_num += 1
            puts current_num.to_s + " " + next_num.to_s
        }
        current_num = next_num
    }
end