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)

package main;
import java.io.BufferedWriter;
import java.io.File;
import java.io.FileWriter;
import java.io.IOException;
import java.io.PrintWriter;
import java.util.Scanner;
public class Main{

	public static void main(String[] args){
		//writeInput();
		solve();
		}

	public static void solve(){
		Scanner sc = new Scanner(System.in);

		int N = Integer.parseInt(sc.next());
		int M = Integer.parseInt(sc.next());

		boolean[] isFrom1 = new boolean[N];
		boolean[] isFromN = new boolean[N];

		for(int i = 0;i<M;i++){
			int ai = Integer.parseInt(sc.next());
			int bi = Integer.parseInt(sc.next());
			if(ai==1){
				isFrom1[bi]=true;
			}
			if(bi==N){
				isFromN[ai]=true;
			}
		}
		//System.out.println(M);
		boolean routeExists =false;for(int i=0;i<N;i++)routeExists|=(isFrom1[i]&&isFromN[i]);
		answer(routeExists);
		sc.close();

	}

	public static void answer(boolean b){
		String yes =new String("POSSIBLE");
		String no =new String("IMPOSSIBLE");
		System.out.println(b?yes:no);
	}


	public static void writeInput(){
		try{
			File file = new File("c:\\Users\\jugem\\Documents\\pleiades\\input.dat");
			if (checkBeforeWritefile(file)){
				PrintWriter pw = new PrintWriter(new BufferedWriter(new FileWriter(file)));
				pw.println("5 5");
				pw.println("1 3");
				pw.println("2 3");
				pw.println("2 4");
				pw.println("4 5");
				pw.println("1 4");
				pw.close();
			}
		}catch(IOException e){
			System.out.println(e);
		}
	}

	public static boolean checkBeforeWritefile(File f){
		return f.exists()?(f.isFile()&&f.canWrite()):false;
	}

}