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: Memory Limit Exceeded)

object Main{

  // 次の行き先のリストをもらってきてそれに言って次のリストを問い合わせる
  var ans: Boolean = false

  def check(arr: Array[Array[Int]], now: Int = 0, count: Int = 0): Unit ={
    if(count > 2) ans = ans || false
    else if(now == arr.size - 1) ans = ans || true
    arr(now).zipWithIndex.filter(n => n._1 == 1).foreach(n => check(arr, n._2, count + 1))
  }

  def main(args:Array[String]) = {
    val map = scala.io.Source.stdin.getLines().toList
    val listTmp = map.head.split(" ").map(_.toInt)
    val mapTmp = map.tail
    var arr:Array[Array[Int]] = Array.ofDim[Int](listTmp(0), listTmp(0))
    for(s <- mapTmp){
      var tmpString = s.split(" ")
      arr(tmpString(0).toInt - 1)(tmpString(1).toInt -1) = 1
    }
    check(arr)
    if(ans) println("POSSIBLE")
    else println("IMPOSSIBLE")
  }
}