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: Time Limit Exceeded)

import Control.Arrow
import Control.Monad
import Data.List
import qualified Data.ByteString.Char8 as B

main :: IO ()
main = readLine >>= printRes . solve
    where
        printRes (m, vs)
            | m == -1 = print m
            | otherwise = print m >> mapM_ (putStrLn . unwords . map show) vs

solve :: [Int] -> (Int, [[Int]])
solve [n, k] 
    | k > an = (-1, [])
    | otherwise = (m, es)
    where
        an = ((n - 2) * (n - 1)) `div` 2
        m = n - 1 + an - k 
        es = addEdges base (an - k) 2 3
        base = map (\x -> [1, x]) [2..n] 
        addEdges acc c v u
            | u > n = addEdges acc c (v + 1) (v + 2)
            | c > 0 = addEdges ([v, u] : acc) (c - 1) v (u + 1)
            | otherwise = acc

readLine :: IO [Int]
readLine = unfoldr (fmap (second (maybe B.empty snd . B.uncons)) . B.readInt) <$> B.getLine

readContents :: Int -> IO [[Int]]
readContents = flip replicateM readLine