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.ArrayDeque;
import java.util.ArrayList;
import java.util.Scanner;

public class Main {

	public static void main(String[] args) {
		Main main = new Main();
		main.run();
	}

	class Pair{
		int i;
		int cnt;
		public Pair(int i, int cnt) {
			this.i=i;
			this.cnt=cnt;
		}
	}

	public void run() {
		Scanner sc = new Scanner(System.in);
		int n=sc.nextInt();
		int m=sc.nextInt();
		ArrayList<ArrayList<Integer>> a = new ArrayList<>();
		for(int i=0; i<=n; i++) {
			a.add(new ArrayList<Integer>());
		}
		for(int i=0; i<m; i++) {
			int s = sc.nextInt();
			int t = sc.nextInt();
			a.get(s).add(t);
		}
		ArrayDeque<Pair> stack = new ArrayDeque<Pair>();
		stack.add(new Pair(1,0));
		boolean ok = false;

		while(!stack.isEmpty()) {
			Pair p = stack.pop();
			if(p.i == n && p.cnt == 2) {
				ok=true;
				break;
			}
			for(int t : a.get(p.i)) {
				stack.add(new Pair(t, p.cnt+1));
			}
		}
		if(ok) {
			System.out.println("POSSIBLE");
		} else {
			System.out.println("IMPOSSIBLE");
		}
		sc.close();
	}
}