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 Haskell (GHC 7.10.3) (judge verdict: Wrong Answer)

import Data.Graph.Inductive.Graph
import Data.List
import Data.Graph.Inductive.PatriciaTree

main = do
  [n,k]<-map read.words<$>getLine
  putStr $ solve n k

solve n k = case ans of
  Nothing -> "-1"
  Just g -> toAns g
  where
  ans = go k addingEdges (mkUGraph [1..n] []) :: (Maybe (Gr () ()))
  addingEdges = [(a,b,())|a<-[1..n-1],b<-[a+1..n-1]]
  go 0 _ g = Just g
  go _ [] _ = Nothing
  go k (e:es) g = go (k-1) es (insEdge e g)
  toAns = unlines . con . map f . go es . sort . edges
    where
    go es [] = es
    go []  _ = []
    go (e:es) (r:rs)
      | e == r = go es rs
      | otherwise = e : go es (r:rs)
    f (a,b) = unwords $ map show [a,b]
    es = [(a,b)|a<-[1..n-1],b<-[a+1..n-1]]
    con es = show (length es):es