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: Time Limit Exceeded)

using System;
using static System.Console;
using System.Collections.Generic;

public class Test
{
	static int n,m;
	static List<int> a;
	static List<int> b;
	static List<int> viaIndex;
	static List<int> viaStation;
		        
	public static void Main()
	{
					            
		var input1=ReadLine().Split();
		n=int.Parse(input1[0]);
		m=int.Parse(input1[1]);
		a=new List<int>(m);
		b=new List<int>(m);
		viaIndex=new List<int>(m);
		viaStation=new List<int>(m);
		for(var i=0;i<m;i++)
		{
			var input2=ReadLine().Split();
			a.Add(int.Parse(input2[0]));
			b.Add(int.Parse(input2[1]));
		}

		for(var i=0;i<m;i++)
		{
			if(a[i]==1)
			{
				viaIndex.Add(i);
				viaStation.Add(b[i]);
			}
		}
		
		for(var i=0;i<m;i++)
		{
			if(b[i]==n && viaStation.Contains(a[i]))
			{
				WriteLine("POSSIBLE");
				return;
			}
		}

		WriteLine("IMPOSSIBLE");
	}
}