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)

-- https://github.com/minoki/my-atcoder-solutions
{-# LANGUAGE BangPatterns #-}
import Data.Char (isSpace)
import Data.List (unfoldr)
import Control.Monad (forM_)
import qualified Data.ByteString.Char8 as BS

main = do
  [n,k] <- unfoldr (BS.readInt . BS.dropWhile isSpace) <$> BS.getLine
  let m = (n - 1) * (n - 2) `quot` 2
  if k > m
    then putStrLn "-1"
    else do let l = m - k
            print $ n - 1 + l
            forM_ [2..n] $ \i -> do
              putStrLn $ unwords ["1", show i]
            let loop 0 !i !j = return ()
                loop l !i !j | j > n = loop l (i+1) (i+2)
                           | otherwise = do putStrLn $ unwords [show i, show j]
                                            loop (l - 1) i (j + 1)
            loop l 2 3