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 CSharpSample01
{
    

    class Program
    {

        static List<int>[] portlist;


        static void Main(string[] args)
        {
            string[] str = Console.ReadLine().Split(' ');
            int N = int.Parse(str[0]);
            int M = int.Parse(str[1]);

            portlist = new List<int>[N];

            for(int i = 0; i < N; i++)
            {
                portlist[i] = new List<int>();
            }
            

            for(int i = 0; i < M; i++)
            {
                string[] input = Console.ReadLine().Split(' ');
                int a = int.Parse(input[0]) - 1;
                int b = int.Parse(input[1]) - 1;

                portlist[a].Add(b);
                portlist[b].Add(a);
            }
            
            for(int i = 1; i < N - 1; i++)
            {
                bool flag0 = false;
                bool flagN = false;

                for(int j = 0; j < portlist[i].Count; j++)
                {
                    if(portlist[i][j] == 0)
                    {
                        flag0 = true;
                    }
                    else if(portlist[i][j] == N - 1)
                    {
                        flagN = true;
                    }

                    if(flag0 && flagN)
                    {
                        Console.WriteLine("POSSIBLE");
                        return;
                    }

                }

            }

            Console.WriteLine("IMPOSSIBLE");

        }
    }
}