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: Wrong Answer)

import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.ArrayDeque;
import java.util.ArrayList;
import java.util.Deque;

public class Main {

	static ArrayList<Integer> alredy = new ArrayList<>();
	static Deque<Integer> stack = new ArrayDeque<>();
	static ArrayList<ArrayList<Integer>> list = new ArrayList<ArrayList<Integer>>();

	// static int count = 0;
	static int n;

	static boolean flag = false;

	public static void main(String args[]) throws IOException {
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));

		String str[] = br.readLine().split(" ");
		n = Integer.parseInt(str[0]);
		int m = Integer.parseInt(str[1]);

		for (int i = 0; i < n; i++) {
			list.add(new ArrayList<>());
		}

		for (int i = 0; i < m; i++) {
			str = br.readLine().split(" ");
			int a = Integer.parseInt(str[0]);
			int b = Integer.parseInt(str[1]);
			list.get(a - 1).add(b - 1);
		}
		dfs(0);
		if (flag) {
			System.out.println("POSSIBLE");
		} else {
			System.out.println("IMPOSSIBLE");
		}
	}

	static void dfs(int a) {
		stack.add(a);
		int count = 0;
		count++;
		while (!stack.isEmpty()) {
			int next = stack.poll();
			alredy.add(next);
			for (int i = 0; i < list.get(next).size(); i++) {
				int b = list.get(next).get(i);
				if (count < 2) {
					if (b == n - 1) {
						flag = true;
						break;
					} else {
						dfs(b);
					}
				}
			}
		}
	}
}