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;

namespace AtCoder
{
	class Program
	{
		static void Main(string[] args)
		{
			var Instance = new CatSnukeVoyage();
			Instance.Exec();
		}
	}

	public class CatSnukeVoyage
	{
		public void Exec()
		{
			var nm = Console.ReadLine().Split(' ').Select(i => int.Parse(i)).ToArray();
			int n = nm[0];
			int m = nm[1];
			HashSet<int> ahash = new HashSet<int>();
			HashSet<int> bhash = new HashSet<int>();
			for (var j = 1; j <= m; ++j) {
				var ab = Console.ReadLine().Split(' ').Select(i => int.Parse(i)).ToArray();
				if (ab[0] == 1) {
					ahash.Add(ab[1]);
				}

				if (ab[1] == n) {
					bhash.Add(ab[0]);
				}
			}

			bool canVoyage = false;

			foreach (var a in ahash) {
				if (bhash.Contains(a)) {
					canVoyage = true;
				}
			}

			string result = canVoyage ? "POSSIBLE" : "IMPOSSIBLE";
			Console.WriteLine(result);
			Console.Out.Flush();
			Console.ReadKey();
		}
	}
}