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 inputs = readInputLine().split(" ").map { Integer.parseInt(it) }
    val n = inputs[0]
    val k = inputs[1]
    
    // うにの場合の最大数を超えるKはありえない
    // 最大数は1 to (N-1)までの総和
    if (k > (n - 1) * (n - 2) / 2) {
        println("-1")
        return
    }
    
    // 辺の本数を出す
    println("${n - 1 + (n - 1) * (n - 2) / 2 - k}")
    
    // まずはうにを構成する辺を作る
    for (i in 2..n) {
        println("1 $i")
    }
    
    // 条件を満たす点を減らす辺を生やす
    var s = 2
    var e = 3
    for (i in 1..(n - 1) * (n - 2) / 2 - k) {
        println("$s $e")
        e++
        if (e > n) {
            s++
            e = s + 1
        }
    }
}
 
fun readInputLine(): String {
    return readLine()!!
}