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: Accepted)

n,k = gets.split.map(&:to_i)
if (n-1)*(n-2)/2 < k
    puts "-1"
    exit
end
if n == 2 && k == 0
    puts 1,"1 2"
    exit
end
if k < n-2
    ans = []
    (n-k-2).times do |i|
        (n-i-1).times do |j|
            ans << [i+1,i+j+2]
        end
    end
    (k+1).times do |i|
        ans << [n-i,n-i-1]
    end
else
    sum = (n-1)*(n-2)/2
    m = n-1
    # while (1)
    100.times do
        if (sum-(m-2) <= k)
            break
        else
            sum -= m-2
            m -= 1
        end
    end
    ans = []
    m.times do |i|
        ans << [1,i+2]
    end
    ((m+2)..n).each do |i|
        ans << [i-1,i]
    end
    (sum-k).times do |i|
        ans << [2,i+3]
    end
end
s = ans.size
puts s
s.times do |i|
    puts ans[i].join(" ")
end