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) {
		Main main = new Main();
		main.run();
	}

	ArrayList<ArrayList<Integer>> g = new ArrayList<>();
	int dist[];
	boolean used[];
	int INF = 1001001001;
	public void run() {
		Scanner sc = new Scanner(System.in);
		int n=sc.nextInt();
		int m=sc.nextInt();
		for(int i=0; i<n; i++) {
			g.add(new ArrayList<>());
		}
		dist = new int[n];
		for(int i=0; i<n; i++) {
			dist[i]=INF;
		}
		used = new boolean[n];
		for(int i=0; i<m; i++) {
			int a=sc.nextInt();
			int b=sc.nextInt();
			a--;
			b--;
			g.get(a).add(b);
			g.get(b).add(a);
		}
		bfs(0,0);
		if(dist[n-1]<=2) {
			System.out.println("POSSIBLE");
		}else {
			System.out.println("IMPOSSIBLE");
		}
		sc.close();
	}


	public void bfs(int p, int d) {
		ArrayDeque<Integer> q = new ArrayDeque<>();
		q.add(p);
		dist[p]=0;
		used[p]=true;
		while(!q.isEmpty()) {
			int s = q.poll();
			for(int i=0; i<g.get(s).size(); i++) {
				int t = g.get(s).get(i);
				if(used[t]) continue;
				used[t]=true;
				dist[t]=dist[s]+1;
				q.add(t);
			}
		}
	}


}