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 Java8 (OpenJDK 1.8.0) (judge verdict: Runtime Error)

import java.util.*;

/**
 * Created by mizuk on 2017/07/26.
 */
public class Main {
    private static int N;
    private static int M;
    private static ArrayList<Integer> a = new ArrayList<Integer>();
    private static ArrayList<Integer> b = new ArrayList<Integer>();
    private static ArrayList<Integer> a2b = new ArrayList<Integer>();
    private static ArrayList<Integer> b2a = new ArrayList<Integer>();

    public static void input(){
        Scanner scan = new Scanner(System.in);
        N = scan.nextInt();
        M = scan.nextInt();

        for(int i=0;i<M;i++) {
            a.add(scan.nextInt());
            b.add(scan.nextInt());
        }
    }

    public static void main(String args[]){
        //入力
        input();

        for(int i=0;i<a.size();i++){
            if(a.get(i) == 1){
                a2b.add(b.get(i));
            }
            if(b.get(i) == N){
                b2a.add(a.get(i));
            }
        }

        for (int i : a2b){
            for (int j : b2a){
                if(a2b.get(i) == b2a.get(j)){
                    System.out.println("POSSIBLE");
                    return;
                }
            }
        }

        System.out.println("IMPOSSIBLE");
    }
}