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 Java (OpenJDK 11.0.6) (judge verdict: Accepted)

import java.util.*;
 
public class Main {
	public static void main(String[] args) throws Exception{
		Scanner sc = new Scanner(System.in);
		int n = sc.nextInt();
        int m = sc.nextInt();
        int[] a = new int[m];
        int[] b = new int[m];
        Set<Integer> mid = new HashSet<>(); 
        Set<Integer> goal = new HashSet<>(); 
        for(int i = 0; i < m; i++){
        	a[i] = sc.nextInt();
            b[i] = sc.nextInt();
            if(a[i] == 1){
            	mid.add(b[i]);
            }else if(b[i] == n){
            	goal.add(a[i]);
            }
        }
        ArrayList<Integer> list = new ArrayList<>();
        for(int x : goal){
        	list.add(x);
        }
        for(int i = 0; i < list.size(); i++){
            if(mid.contains(list.get(i))){
            	System.out.println("POSSIBLE");
                return;
            }
        }
        System.out.println("IMPOSSIBLE");
	}
}