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.*;
import java.lang.*;
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];
		int count1 = 0,count2 = 0;
		int[] fromOne = new int[M];
		int[] toN = new int[M];      
		for( int i=0; i<M; i++ ){
			a[i] = sc.nextInt();
			b[i] = sc.nextInt();
			if( a[i]==1 ){
				fromOne[count1] = b[i];
				count1++;
            }
			if( b[i]==N ){
				toN[count2] = a[i];
				count2++;              
            }              
		}
		loop:for( int i=0; i<count1; i++ ){
			for( int j=0; j<count2; j++ ){          
				if( fromOne[i]==toN[j] ){
					System.out.println("POSSIBLE");
					break loop;
				}
            }              
			if( i==count1-1 ){
				System.out.println("IMPOSSIBLE");
			}
		}
	}
}