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: Time Limit Exceeded)


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

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();

        Set<Integer> set_1 = new HashSet<Integer>();
        Set<Integer> set_N = new HashSet<Integer>();



        for(int i = 0; i < m; i++){
        	int a = sc.nextInt();
        	int b = sc.nextInt();

        	if(a == 1){
        		set_1.add(b);
        	}

        	if(b == n){
        		set_N.add(a);
        	}
        }

        //System.out.printf("%d\n",input[0][0]);

        boolean isPossible = false;

        for (int ary:set_1)
        {
        	for(int ary_n:set_N)
        	{
        		if(ary == ary_n)
        		{
        			isPossible = true;
break;
        		}
        	}

        }


        if(isPossible){
        	System.out.printf("POSSIBLE");
        }else{
        	System.out.printf("IMPOSSIBLE");
        }

    }

}