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 Scala (2.11.7) (judge verdict: Wrong Answer)

import scala.io.StdIn
import scala.collection.mutable._

object Main extends App {

  val Array(n, m) = StdIn.readLine.split(" ").map(_.toInt)
  val a = Iterator.continually(StdIn.readLine)
    .take(m)
    .map(_.split(" ").map(_.toInt))
    .toArray

  val graph = Array.fill(n+1)(ListBuffer.empty[Int])
  a.foreach(e => {
    graph(e(0)) += e(1)
  })

  val visit = Array.ofDim[Boolean](n+1)
  def dfs(pos:Int, cnt:Int):Unit = {
    if(cnt < 0) return
    visit(pos) = true
    print(pos + " ")
    for(i <- graph(pos)) {
      dfs(i, cnt-1)
    }
  }

  dfs(1,2)
  val ans = if(visit(n)) "POSSIBLE" else "IMPOSSIBLE"
  println(ans)
}