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: Time Limit Exceeded)

import Data.List
import Control.Monad

main = do
    [n, m] <- map readInt . words <$> getLine
    xs <- map (\x -> map readInt $ words x) <$> replicateM m getLine

    putStrLn $ if findRoute 1 n 1 xs n
        then "POSSIBLE"
        else "IMPOSSIBLE"

    where
        readInt = read :: String -> Int
        findRoute i j t xs n
            | t > 2 = False
            | elem [i, j] xs = True
            | elem [j, i] xs = True
            | all (\x -> x !! 0 /= i) xs = False
            | all (\x -> x !! 1 /= j) xs = False
            | otherwise = any
                (\k -> (findRoute i k (t + 1) xs n) && (findRoute j k (t + 1) xs n))
                $ [1 .. n] \\ [i, j]