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;
using System.Text;

public class MainClass
{
	public const long Giri = 1000000007;
	public const long DpInf = 99999999999999;
	
	class Island
	{
		public List<int> Ships {get;set;}
		public int Distance {get;set;}
	}
	public static void Main(string[] args)
	{
		var p = Input().ToInt();
		var n = p[0];
		var m = p[1];
		var islands = new Island[n];
		for(int i = 0; i < n; i++)
			islands[i] = new Island(){Ships=new List<int>(), Distance = int.MaxValue};
			
		for(int i = 0; i < m; i++)
		{
			p = Input().ToInt(-1);
			islands[p[1]].Ships.Add(p[0]);
			islands[p[0]].Ships.Add(p[1]);
		}
		
		DFS(0, islands, 0);
		if(islands[n-1].Distance == 2)
		{
			Console.WriteLine("POSSIBLE");
		}
		else
		{
			Console.WriteLine("IMPOSSIBLE");
		
		}
	}
	static void DFS(int index, Island[] islands, int deep)
	{
		if(deep > 3) return;
		if(islands[index].Distance <= deep)
			return;
		islands[index].Distance = deep;
		foreach(var k in islands[index].Ships)
		{
			DFS(k, islands, deep+1);
		}
	}
	
	static long GCD(long a, long b)
	{
		var v = new[] { a, b };
		while (v[1] != 0) { v = new[] { v[1], v[0] % v[1] }; }
		return v[0];
	}
	public static string[] Input() { return Console.ReadLine().Split(); }
}

public static class Smarter
{
	public static int ToInt(this string str) { return int.Parse(str); }
	public static long ToLong(this string str) { return long.Parse(str); }
	public static int[] ToInt(this string[] str, int offset = 0)
	{
		var r = new int[str.Length];
		for(int i = 0; i < str.Length; i++) r[i] = str[i].ToInt() + offset;
		return r;
	}
}