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"
	"math"
	"os"
	"strconv"
)

var isProduct = false

func main() {
	nextReader = newScanner()

	n := nextInt()
	k := nextInt()

	// 中心点1を除く、(n-1)個の頂点から(n-1-1)個の頂点に辺が引けて、重複をなくすため2で割る
	max := (n - 1) * (n - 2) / 2

	if k > max {
		fmt.Println("-1")
		return
	}

	//間引く本数
	delta := max - k

	fmt.Println(delta + n)

	for i := 1 + 1; i < n+1; i++ {
		fmt.Println(1, i)
	}

	for j := 0; j < delta; j++ {
		fmt.Println(j+2, j+3)
	}

}

/* --------------------------------------------------------------------------
 *  sort
 * ------------------------------------------------------------------------- */

// type S struct {
//   sort int
// }
// type Sorter []S

// func (a Sorter) Len() int           { return len(a) }
// func (a Sorter) Swap(i, j int)      { a[i], a[j] = a[j], a[i] }
// func (a Sorter) Less(i, j int) bool { return a[i].sort < a[j].sort }

// type Sorter []Sortable

// func (a Sorter) Len() int           { return len(a) }
// func (a Sorter) Swap(i, j int)      { a[i], a[j] = a[j], a[i] }
// func (a Sorter) Less(i, j int) bool { return a[i].Axis < a[j].Axis }

/* --------------------------------------------------------------------------
 *  math
 * ------------------------------------------------------------------------- */
func lcm(x, y int) int {
	return x * y / gcd(x, y)
}

func gcd(x, y int) int {
	tmp := x % y
	if tmp > 0 {
		return gcd(y, tmp)
	} else {
		return y
	}
}

func abs(i int) int {
	return int(math.Abs(float64(i)))
}

/* --------------------------------------------------------------------------
 *  debug
 * ------------------------------------------------------------------------- */
func debugln(s ...interface{}) {
	if !isProduct {
		fmt.Println(s...)
	}
}

func debug(s ...interface{}) {
	if !isProduct {
		fmt.Print(s...)
	}
}
func debugf(f string, s ...interface{}) {
	if !isProduct {
		fmt.Printf(f, s...)
	}
}

/* --------------------------------------------------------------------------
 *  std.io
 * ------------------------------------------------------------------------- */
var nextReader func() string

func newScanner() func() string {
	r := bufio.NewScanner(os.Stdin)
	r.Buffer(make([]byte, 1024), int(1e+11))
	r.Split(bufio.ScanWords)
	return func() string {
		r.Scan()
		return r.Text()
	}
}
func nextString() string {
	return nextReader()
}
func nextInt64() int64 {
	v, _ := strconv.ParseInt(nextReader(), 10, 64)
	return v
}
func nextInt() int {
	v, _ := strconv.Atoi(nextReader())
	return v
}
func nextInts(n int) []int {
	r := make([]int, n)
	for i := 0; i < n; i++ {
		r[i] = nextInt()
	}
	return r
}
func nextInt64s(n int) []int64 {
	r := make([]int64, n)
	for i := 0; i < n; i++ {
		r[i] = nextInt64()
	}
	return r
}
func nextFloat64() float64 {
	f, _ := strconv.ParseFloat(nextReader(), 64)
	return f
}

func maxInt(a, b int) int {
	if a > b {
		return a
	} else {
		return b
	}
}

/* --------------------------------------------------------------------------
 *  memo
 * ------------------------------------------------------------------------- */