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 System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;

namespace _068_2
{
    class Program
    {
        static void Main(string[] args)
        {
            string[] strNM = Console.ReadLine().Split(' ');

            int N = int.Parse(strNM[0]);
            int M = int.Parse(strNM[1]);

            List<Tuple<int, int>> shipList = new List<Tuple<int, int>>();

            for (int i = 0; i < M; i++)
            {
                strNM = Console.ReadLine().Split(' ');

                shipList.Add(Tuple.Create(int.Parse(strNM[0]), int.Parse(strNM[1])));
            }

            string ans = "IMPOSSIBLE";

            if (!shipList.Any(x=>x.Item2 == N))
            {
                Console.Write(ans);
                return;
            }

            List<int> posibleStartList = shipList.Where(x => x.Item2 == N).Select(x=>x.Item1).ToList();

            if (shipList.Where(x => x.Item1 == 1).Any(x => posibleStartList.Contains(x.Item2)))
            {
                ans = "POSSIBLE";
            }

            Console.WriteLine(ans);
        }

    }
}