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.stream.IntStream;

public class Main{
	static final Scanner s=new Scanner(System.in);
	static IntStream REPS(int v){return IntStream.range(0,v);}
	static IntStream REPS(int l,int r){return IntStream.rangeClosed(l,r);}
	static IntStream INS(int n){return REPS(n).map(i->getInt());}
	static int getInt(){return Integer.parseInt(s.next());}

	public static void main(String[]$){
		int n=getInt(),m=getInt();
		HashSet<Integer> ione=new HashSet<>(),in=new HashSet<>();

		for(int i=0;i<m;++i) {
			int a=getInt(),b=getInt();
			if(a==1)
				ione.add(b);
			if(b==1)
				ione.add(a);
			if(a==n)
				in.add(b);
			if(b==n)
				in.add(a);
		}

		System.out.println(
				ione.stream().anyMatch(in::contains)
				?"POSSIBLE":"IMPOSSIBLE"
				);
	}
}