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: Accepted)

import scala.collection.mutable.ArrayBuffer

object Main {
  def main(args: Array[String]): Unit = {
    solve2
  }

  def solve2(): Unit = {
    val sc = new java.util.Scanner(System.in)
    val n, m = sc.nextInt
    val firstCon = scala.collection.mutable.Set[Int]()
    val lastCon = scala.collection.mutable.Set[Int]()
    val con = Array.fill[ArrayBuffer[Int]](n)(new ArrayBuffer[Int]())
    for (i <- 0 until m) {
      val a = sc.nextInt
      val b = sc.nextInt

      if (a == 1) firstCon += b
      if (b == n) lastCon += a
    }

    println(if ((firstCon & lastCon).nonEmpty) "POSSIBLE" else "IMPOSSIBLE")

  }


  def solve(): Unit = {
    val sc = new java.util.Scanner(System.in)
    val n, m = sc.nextInt
    val con = Array.fill[ArrayBuffer[Int]](n)(new ArrayBuffer[Int]())
    for (i <- 0 until m) {
      val a = sc.nextInt - 1
      val b = sc.nextInt - 1
      con(a).append(b)
      con(b).append(a)
    }

    val destNum = n - 1
    var ans = false
    for (num <- con(0)) {
      if (con(num).contains(destNum)) {
        ans = true
      }
    }

    println(if (ans) "POSSIBLE" else "IMPOSSIBLE")

  }
}