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.Arrays;
import java.util.Scanner;

public class Main{

	public static void main(String[] args) {
		Scanner scn = new Scanner(System.in);
		int N = scn.nextInt();
		int M = scn.nextInt();
		Ship[] S = new Ship[M];
		for(int i = 0;i < M;i++) {
			S[i] = new Ship(scn.nextInt(), scn.nextInt());
		}
		Arrays.sort(S);

		boolean[] Go = new boolean[N];
		for(int i = 0;i < M;i++) {
			if(S[i].getA() == 1) {
				Go[S[i].getB()-1] = true;
			}
			if(S[i].getB()==N) {
				if(Go[S[i].getA()-1])Go[N-1] = true;
			}
			if(Go[N-1])break;
		}


		System.out.println(Go[N-1]?"POSSIBLE":"IMPOSSIBLE");
	}

}

class Ship implements Comparable<Ship>{
	int a;
	int b;

	Ship(int a, int b){
		this.a = a;
		this.b = b;
	}

	@Override
	public int compareTo(Ship o) {
		if(this.a > o.getA())return 1;
		if(this.a < o.getA())return -1;
		return 0;
	}

	public int getA() {
		return a;
	}
	public int getB() {
		return b;
	}

}