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: Time Limit Exceeded)

case class Node(id: Int) {
  var edges: Set[Node] = Set.empty
}

class Graph(val nodes: Set[Node]) {
  def pathExists(start: Node, end: Node, maxDistance: Int): Boolean = {
    val queue = collection.mutable.Queue((0, start))
    var seenNodes: Set[Node] = Set.empty

    while (!queue.isEmpty) {
      val (distance, node) = queue.dequeue
      if (node == end) {
        return true
      }
      if (distance + 1 <= maxDistance) {
        seenNodes += node
        val nextNodes = node.edges.diff(seenNodes).map(n => (distance + 1, n))
        queue.enqueue(nextNodes.toSeq: _*)
      }
    }
    false
  }
}

object Main {
  def main(args: Array[String]): Unit = {
    val Array(n, m) = io.StdIn.readLine.split(" ").map(_.toInt)
    val nodes = (1 to n).map(v => Node(v)).toSet
    val graph = new Graph(nodes)
    (1 to m).foreach { _ =>
      val Array(a, b) = io.StdIn.readLine.split(" ").map(n => Node(n.toInt))
      graph.nodes.find(_ == a).foreach(_.edges += graph.nodes.find(_ == b).get)
    }
    val start = graph.nodes.find(_ == Node(1)).get
    val end = graph.nodes.find(_ == Node(n)).get
    if (graph.pathExists(start, end, 2)) {
      println("POSSIBLE")
    } else {
      println("IMPOSSIBLE")
    }
  }
}