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.Text;

namespace AtTest.C_Challenge
{
    class ABC_068
    {
        static void Main(string[] args)
        {
            Method(args);
            Console.ReadLine();
        }

        static void Method(string[] args)
        {
            string[] input = Console.ReadLine().Split(' ');
            int n = int.Parse(input[0]);
            int m = int.Parse(input[1]);

            var stoppings = new Dictionary<int, bool>();
            var abs = new int[m][];
            for (int i = 0; i < m; i++)
            {
                int[] ab= ReadInts();
                abs[i] = new int[2];
                abs[i][0] = ab[0];
                abs[i][1] = ab[1];
            }
            Array.Sort(abs, (a, b) => a[0] - b[0]);

            for(int i = 0; i < m; i++)
            {
                if (abs[i][0] == 1)
                {
                    stoppings.Add(abs[i][1], true);
                }
                else
                {
                    if (abs[i][1] == n&&stoppings.ContainsKey(abs[i][0]))
                    {
                        Console.WriteLine("POSSIBLE");
                        return;
                    }
                }
            }

            Console.WriteLine("IMPOSSIBLE");
        }

        private static string Read() { return Console.ReadLine(); }
        private static int ReadInt() { return int.Parse(Read()); }
        private static long ReadLong() { return long.Parse(Read()); }
        private static double ReadDouble() { return double.Parse(Read()); }
        private static int[] ReadInts() { return Array.ConvertAll(Read().Split(), int.Parse); }
        private static long[] ReadLongs() { return Array.ConvertAll(Read().Split(), long.Parse); }
        private static double[] ReadDoubles() { return Array.ConvertAll(Read().Split(), double.Parse); }
    }
}