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 C# (Mono 4.6.2.0) (judge verdict: Accepted)

using System;
using System.Collections.Generic;
using System.Linq;
class Program
{
    static void Main()
    {
        string[] s = Console.ReadLine().Split(' ');
        int n, m;
        n = int.Parse(s[0]);
        m = int.Parse(s[1]);
        Graph g = new Graph(n);
        for (int i = 0; i < m; i++)
        {
            s = Console.ReadLine().Split(' ');
            int a, b;
            a = int.Parse(s[0]);
            b = int.Parse(s[1]);
            g.SetEdge(a, b);
            g.SetEdge(b, a);
        }
        bool f = false;
        foreach (var e in g.node[0].edge)
        {
            f = f || e.G.Child.Contains(g.node[n - 1]);
            if (f)
                break;
        }
        Console.WriteLine(f ? "POSSIBLE" : "IMPOSSIBLE");
    }
}
class Node
{
    public int id;
    public List<Edge> edge = new List<Edge>();
    public List<Node> Child = new List<Node>();
    public Node(int id) { this.id = id; }
}
class Edge
{
    public Node S;
    public Node G;
    public Edge(Node S, Node G)
    {
        this.S = S;
        this.G = G;
    }
}
class Graph
{
    public Node[] node;
    public Graph(int n)
    {
        node = new Node[n];
        for (int i = 0; i < n; i++)
            node[i] = new Node(i + 1);
    }
    public void SetEdge(int n1, int n2)
    {
        if (n1 > node.Length || n1 <= 0 || n2 > node.Length || n2 <= 0)
            return;
        Edge e = new Edge(node[n1 - 1], node[n2 - 1]);
        node[n1 - 1].edge.Add(e);
        node[n1 - 1].Child.Add(node[n2 - 1]);
    }
}