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.Collections.Generic;
using System.Linq;
using System;
class Program
{
	static HashSet<int>[] Edge;

	static void Main()
	{
		var firstLine = Console.ReadLine();
		string[] splitedLine = firstLine.Split(' ');
		int maxIsland = int.Parse(splitedLine[0]);
		int maxBridge = int.Parse(splitedLine[1]);

		Edge = Enumerable.Range(0, maxIsland).Select(i => new HashSet<int>()).ToArray();
		for (int i = 0; i < maxBridge; i++)
		{
			string[] inputsStr = Console.ReadLine().Split(' ');
            int[] inputs = new int[2];
			inputs[0] = int.Parse(inputsStr[0]);
			inputs[1] = int.Parse(inputsStr[1]);
            //Console.WriteLine("inputs[0]: " + inputs[0]);
            //Console.WriteLine("inputs[1]: " + inputs[1]);
            Edge[inputs[0]-1].Add(inputs[1]);
            Edge[inputs[1]-1].Add(inputs[0]);
		}
        bool isPossible = false;
        foreach(var items in Edge[0]){
            foreach(var item in Edge[items-1]){
				//Console.WriteLine("item: " + item);
				//Console.WriteLine("n: " + maxIsland);
                if (item == maxIsland){
                    //Console.WriteLine("Match!");
                    isPossible = true;
                    break;
                }
            }
        }
        if(isPossible){
            Console.WriteLine("POSSIBLE");
        }else{
            Console.WriteLine("IMPOSSIBLE");
        }
    }
}