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;
using System.Text;
using System.Threading.Tasks;

namespace ConsoleApp15
{
    class Class86
    {
        static void Main()
        {
            var NM = Console.ReadLine().Split().Select(int.Parse).ToArray();
            int N = NM[0], M = NM[1];
            HashSet<int> a = new HashSet<int>();
            HashSet<int> b = new HashSet<int>();
            List<Tuple<int, int>> s = new List<Tuple<int, int>>();
            
            for(int i = 0; i < M; i++)
            {
                var r = Console.ReadLine().Split().Select(int.Parse).ToArray();
                if (r[0] == 1)
                {
                    if (!a.Contains(r[1])) a.Add(r[1]);
                    
                }
                else if (r[1] == N)
                {
                    if (!b.Contains(r[0])) b.Add(r[0]);
                }
            }
            foreach(int i in a)
                if (b.Contains(i))
                {
                    Console.WriteLine("POSSIBLE");return;
                }

            Console.WriteLine("IMPOSSIBLE");
        }
    }
}