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: Accepted)

import java.util.HashSet;
import java.util.Scanner;
import java.util.Set;

public class Main {

    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int N = sc.nextInt();
        int M = sc.nextInt();
        int[] A = new int[M];
        int[] B = new int[M];
        for (int i = 0; i < M; i++) {
            A[i] = sc.nextInt();
            B[i] = sc.nextInt();
        }
        System.out.println( solve(N, M, A, B) );
    }

    private static String solve(int N, int M, int[] A, int[] B) {
        Set<Integer> from_1 = new HashSet<>();
        for (int i = 0; i < M; i++) {
            int a = A[i];
            int b = B[i];

            if( a == 1 ) {
                from_1.add(b);
            } else if( b == 1 ) {
                from_1.add(a);
            }
        }

        for (int i = 0; i < M; i++) {
            int a = A[i];
            int b = B[i];

            if( a == N && from_1.contains(b) ) return "POSSIBLE";
            if( b == N && from_1.contains(a) ) return "POSSIBLE";
        }
        return "IMPOSSIBLE";
    }
}