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.*;

public class Main {
    int n, m;
    ArrayList<Integer>[] es;

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

    void read() {
        Scanner sc = new Scanner(System.in);
        n = sc.nextInt();
        m = sc.nextInt();
        es = new ArrayList[n];
        for (int i = 0; i < n; i++)
            es[i] = new ArrayList<>();
        for (int i = 0; i < m; i++) {
            int a = sc.nextInt() - 1;
            int b = sc.nextInt() - 1;
            es[a].add(b);
            es[b].add(a);
        }
    }

    void solve() {
        int[] log = new int[n];
        Arrays.fill(log, Integer.MAX_VALUE);
        PriorityQueue<Node> queue = new PriorityQueue<>(Comparator.comparing(Node::getCost));
        queue.add(new Node(0, 0));
        log[0] = 0;
        while (!queue.isEmpty()) {
            Node a = queue.poll();
            if (log[a.current] < a.cost) continue;
            log[a.current] = a.cost;
            for (int e: es[a.current]) {
                if (log[a.current] + 1  <= 2)
                    queue.add(new Node(e, log[a.current]+1));
            }
        }
        if (log[n-1] <= 2)
            System.out.println("POSSIBLE");
        else
            System.out.println("IMPOSSIBLE");
    }

    private class Node {
        int current;
        int cost;
        Node (int curr, int c) {
            current = curr;
            cost = c;
        }

        public int getCost() {
            return cost;
        }
    }
}