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 Kotlin (1.0.0) (judge verdict: Accepted)

fun main(args: Array<String>) {
    val (n, k) = readLine()!!.split(' ').map(String::toInt)
    val allHn = n * (n - 1) / 2
    if (k > allHn - (n - 1)) {
        println(-1)
        return
    }
    val hn = allHn - k

    val allH = mutableListOf<MutableList<Int>>()
    (1..n).forEach { allH.add(mutableListOf()) }

    for (i in 1 until n) {
        for (j in i + 1..n) {
            allH[i].add(j)
        }
    }
    var deleteNum = 0
    for (i in 1 until (n - 1)) {
        if (deleteNum == k) break
        for (j in i + 1 until n) {
            allH[i].remove(j)
            deleteNum++
            if (deleteNum == k) break
        }
        if (deleteNum == k) break
    }

    println(hn)
    for(i in 1 until n){
        for(j in allH[i]){
            println("$i $j")
        }
    }
}