Problem:
Score : 300 points

Problem Statement

In Takahashi Kingdom, there is an archipelago of N islands, called Takahashi Islands.
For convenience, we will call them Island 1, Island 2, ..., Island N.

There are M kinds of regular boat services between these islands.
Each service connects two islands. The i-th service connects Island a_i and Island b_i.

Cat Snuke is on Island 1 now, and wants to go to Island N.
However, it turned out that there is no boat service from Island 1 to Island N, so he wants to know whether it is possible to go to Island N by using two boat services.

Help him.

Constraints

3 ≤ N ≤ 200 000

1 ≤ M ≤ 200 000

1 ≤ a_i < b_i ≤ N

(a_i, b_i) \neq (1, N)

If i \neq j, (a_i, b_i) \neq (a_j, b_j).

Input

Input is given from Standard Input in the following format:

N M
a_1 b_1
a_2 b_2
:
a_M b_M

Output

If it is possible to go to Island N by using two boat services, print POSSIBLE; otherwise, print IMPOSSIBLE.

Sample Input 1

3 2
1 2
2 3

Sample Output 1

POSSIBLE

Sample Input 2

4 3
1 2
2 3
3 4

Sample Output 2

IMPOSSIBLE

You have to use three boat services to get to Island 4.

Sample Input 3

100000 1
1 99999

Sample Output 3

IMPOSSIBLE

Sample Input 4

5 5
1 3
4 5
2 3
2 4
1 4

Sample Output 4

POSSIBLE

You can get to Island 5 by using two boat services: Island 1 -> Island 4 -> Island 5.

Solution in Haskell (GHC 7.10.3) (judge verdict: Accepted)

import qualified Data.ByteString.Char8 as BC
import qualified Data.IntMap as M
import Data.Maybe (fromJust)
import Data.List
import Data.Array.IO

main = do
  [n, m] <- map read . words <$> getLine :: IO [Int]
  edge <- (\[x, y] -> zip x y) . transpose <$> getInt2DListBC
  let graph = foldl makeGraph M.empty edge
      neighbor = fromJust $ M.lookup 1 graph
      neighbors = sort . concat $ map (\x -> fromJust $ M.lookup x graph) neighbor
  if n == last neighbors then putStrLn "POSSIBLE"
                         else putStrLn "IMPOSSIBLE"

bsToInt :: BC.ByteString -> Int
bsToInt = fst . fromJust . BC.readInt

getInt2DListBC :: IO [[Int]]
getInt2DListBC = map (map bsToInt . BC.words) . BC.lines <$> BC.getContents

type Graph = M.IntMap [Int]

makeGraph :: Graph -> (Int, Int) -> Graph
makeGraph graph (x, y) =
  let nX = M.lookup x graph
      nY = M.lookup y graph
      vX = if nX == Nothing
             then M.insert x [y] graph
             else M.insert x ((:) y $ fromJust nX) graph
  in if nY == Nothing
        then M.insert y [y] vX
        else M.insert y ((:) x $ fromJust nY) vX