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: Runtime Error)

import java.util.*;

public class Main {
	public static void main(String[] args) throws Exception{
		Scanner scn = new Scanner(System.in);
		int n = scn.nextInt();
      	int m = scn.nextInt();
		int[] a = new int[m];
      	int[] b = new int[m];
		for(int i=0; i<m; i++){
			a[i] = scn.nextInt();
          	b[i] = scn.nextInt();
		}
      	ArrayList<Integer> list = new ArrayList<>();
      	for(int i=0; i<m; i++){
			if(a[i]==1) list.add(b[i]);
          	if(b[i]==n) list.add(a[i]);
		}
      	Collections.sort(list);
      	String ans = "IMPOSSIBLE";
      	for(int i=0; i<list.size(); i++){
          if(list.get(i) == list.get(i+1)){
            ans = "POSSIBLE";
            break;
          }
        }
      	System.out.println(ans);
	}
}