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 Go (1.6) (judge verdict: Wrong Answer)

package main

import (
	"bufio"
	"fmt"
	"os"
	"strconv"
)

func getScanner(fp *os.File) *bufio.Scanner {
	scanner := bufio.NewScanner(fp)
	scanner.Split(bufio.ScanWords)
	scanner.Buffer(make([]byte, 500001), 500000)
	return scanner
}

func getNextString(scanner *bufio.Scanner) string {
	scanner.Scan()
	return scanner.Text()
}

func getNextInt(scanner *bufio.Scanner) int {
	i, _ := strconv.Atoi(getNextString(scanner))
	return i
}

func main() {
	fp := os.Stdin
	if len(os.Args) > 1 {
		fp, _ = os.Open(os.Args[1])
	}

	scanner := getScanner(fp)
	writer := bufio.NewWriter(os.Stdout)

	n := getNextInt(scanner)
	k := getNextInt(scanner)

	g := make([][]int, n)
	m := 0
	for i := 0; i < n-1; i++ {
		g[i] = make([]int, n)
		for ii := i + 1; ii < n; ii++ {
			g[i][ii] = 1
			m++
		}
	}
	if k == 0 {
		fmt.Fprintln(writer, m)
		ans := answer(m, n, g)
		for k := 0; k < m; k++ {
			fmt.Fprintln(writer, ans[k])
		}
		writer.Flush()
		return
	}

	for i := 0; i < n-1; i++ {
		exists := false
		for ii := i + 1; ii < n; ii++ {
			if g[i][ii] == 1 {
				if exists == false {
					exists = true
					continue
				}
				k--
				m--
				g[i][ii] = 0
				if k == 0 {
					fmt.Fprintln(writer, m)
					ans := answer(m, n, g)
					for k := 0; k < m; k++ {
						fmt.Fprintln(writer, ans[k])
					}
					writer.Flush()
					return
				}
			}
		}
	}

	fmt.Fprintln(writer, -1)
	writer.Flush()
}

func answer(m, n int, g [][]int) []string {
	ans := make([]string, m)
	a := 0
	for i := 0; i < n-1; i++ {
		for ii := i + 1; ii < n; ii++ {
			if g[i][ii] == 1 {
				ans[a] = fmt.Sprintf("%d %d", i+1, ii+1)
				a++
			}
		}
	}
	return ans
}