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)

object Main extends App {
	val NM = scala.io.StdIn.readLine.split(" ").map(_.toInt)

	val a = new Array[Int](NM(1))
	val b = new Array[Int](NM(1))

	for(i<-0 until NM(1)){
		val t = scala.io.StdIn.readLine.split(" ").map(_.toInt)
		a(i) = t(0)
		b(i) = t(1)
	}

	def find(N: Int, M: Int, a: Array[Int], b: Array[Int]): Boolean = {
		for(i<-0 until M){
			if(a(i) == 1){
				for(j<-0 until M){
					if(a(j) == b(i) && b(j) == N) return true
				}
			}
		}
		return false
	}

	if(find(NM(0), NM(1), a, b)) println("POSSIBLE")
	else println("IMPOSSIBLE")
}