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)

module Main where

import Control.Applicative
import Control.Monad
import Data.List
import qualified Data.Graph as G

bfs :: [G.Tree Int] -> [[Int]]
bfs [] = []
bfs ts = fmap root ts : bfs (concatMap sub ts)
  where
    root (G.Node r _)  = r
    sub  (G.Node _ sf) = sf

main :: IO ()
main = do
    [n, m] <- fmap read . words <$> getLine :: IO [Int]
    as <- replicateM m $ do
        [a, b] <- fmap read. words <$> getLine :: IO [Int]
        return (a, b)

    let g = G.buildG (1, n) as
    let tree = G.dfs g [1]
    let bss = take 3 $ bfs tree

    if length bss < 3
        then putStrLn "IMPOSSIBLE"
        else do
            if any (== n) (bss !! 2)
                then putStrLn "POSSIBLE"
                else putStrLn "IMPOSSIBLE"