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()
	{
		var nm = Array.ConvertAll(Console.ReadLine().Split(new[] { ' ' }), number => int.Parse(number));
		var firsts = new List<int>();
		var routes = new bool[nm[0]];
		for (var i = 0; i < nm[1]; ++i) {
			var a = Array.ConvertAll(Console.ReadLine().Split(new[] { ' ' }), number => int.Parse(number));
			if (a[0] == 1) {
				firsts.Add(a[1] - 1);
			} else if(a[1] == nm[0]) {
				routes[a[0] - 1] = true;
			}
		}

		if (nm[1] > 1) {
			var answer = false;
			foreach (var num in firsts) {
				if (routes[num]) {
					answer = true;
					break;
				}
			}

			Console.WriteLine(answer ? "POSSIBLE" : "IMPOSSIBLE");
		} else {
			Console.WriteLine("IMPOSSIBLE");
		}

		//デバッグ実行での確認用。そのまま提出しても問題なし
		Console.ReadKey();
	}
}