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.IO;
using System.Linq;
using System.Collections.Generic;
using System.Text;

public class Program
{

    public void Proc()
    {
        int[] inpt = Reader.ReadLine().Split(' ').Select(a => int.Parse(a)).ToArray();

        this.IslCount = inpt[0];
        int shipCount = inpt[1];

        for (int i = 0; i < shipCount; i++) {
            inpt = Reader.ReadLine().Split(' ').Select(a => int.Parse(a)).ToArray();
            if(!Ship.ContainsKey(inpt[0])) {
                Ship.Add(inpt[0], new Dictionary<int, bool>());
            }
            if(!Ship.ContainsKey(inpt[1])) {
                Ship.Add(inpt[1], new Dictionary<int, bool>());
            }
            Ship[inpt[0]][inpt[1]] = true;
            Ship[inpt[1]][inpt[0]] = true;
        }

        string ans = "IMPOSSIBLE";
        if(this.CanReach(1, 2)) {
            ans = "POSSIBLE";
        }
        Console.WriteLine(ans);
    
    }

    private int IslCount;

    private bool CanReach(int idx, int remain) {
        if(idx == this.IslCount) {
            return true;
        }
        if(remain<=0) {
            return false;
        }
        if(Ship.ContainsKey(idx)) {
            foreach(int nextIsl in Ship[idx].Keys) {
                if(nextIsl == 1) {
                    continue;
                }
                if(CanReach(nextIsl, remain-1)) {
                    return true;
                }
            }
        }
        return false;
    }
    private Dictionary<int, Dictionary<int, bool>> Ship = new Dictionary<int, Dictionary<int, bool>>();


    public class Reader
	{
		private static StringReader sr;
		public static bool IsDebug = false;
		public static string ReadLine()
		{
			if (IsDebug)
			{
				if (sr == null)
				{
					sr = new StringReader(InputText.Trim());
				}
				return sr.ReadLine();
			}
			else
			{
				return Console.ReadLine();
			}
		}
		private static string InputText = @"



3 2
1 2
2 3

";
	}

	public static void Main(string[] args)
	{
#if DEBUG
		Reader.IsDebug = true;
#endif
		Program prg = new Program();
		prg.Proc();
	}
}