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: Wrong Answer)

import qualified Data.Vector.Unboxed as VU
import qualified Data.Vector.Unboxed.Mutable as VUM
import qualified Data.ByteString.Char8 as BS
import Control.Monad
import Control.Monad.Primitive (PrimState)
import Data.Maybe (fromJust)

main = do
  [n,m] <- map read . words <$> getLine :: IO [Int]
  mv <- VUM.replicate (2*m) (0,0) :: IO (VUM.MVector (PrimState IO) (Int,Int))
  forM_ [1..m] $ \i -> do
    [a,b] <- map (fst . fromJust . BS.readInt) . BS.words <$> BS.getLine 
    VUM.write mv (i-1) (a,b)
    VUM.write mv (m+i-1) (b,a)
  v <- VU.unsafeFreeze mv
  let ones = VU.map snd $ VU.filter ((==1) . fst) v
  print ones
  putStrLn $ if solve ones n v then "POSSIBLE" else "IMPOSSIBLE"
  

solve :: VU.Vector Int -> Int -> VU.Vector (Int,Int) -> Bool
solve ones dest lines = VU.foldl (\b (i,k) -> b || (VU.elem i ones && k==dest)) False lines