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: Accepted)

{-# LANGUAGE BangPatterns #-}
import Control.Arrow
import Control.Monad.Fix
import Data.Char
import Data.Int
import Data.Foldable
import Data.List
import qualified Data.Vector as V
import qualified Data.Vector.Unboxed as VU
import qualified Data.ByteString.Char8 as B
import Debug.Trace

solve :: Int -> Int -> [(Int, Int)]
solve !n !k | k > n1C2  = []
            | otherwise = scatterTo1 ++ drop k edges
 where
  n1C2       = (n - 1) * (n - 2) `div` 2
  edges      = [ (x, y) | x <- [2 .. n - 1], y <- [x + 1 .. n] ]
  scatterTo1 = [ (1, n) | n <- [2 .. n] ]

main = do
  let readInt :: Integral a => B.ByteString -> Maybe (a, B.ByteString)
      readInt = fmap (first fromIntegral . second B.tail) . B.readInt

  (n, k) <-
    (\vec -> (vec VU.! 0, vec VU.! 1)) . VU.unfoldrN 2 readInt <$> B.getLine
  let xs = solve n k

  if null xs
    then print (-1)
    else do
      print $ length xs
      forM_ xs $ \(x, y) -> putStrLn $ show x ++ " " ++ show y