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.Linq.Expressions;
using System.IO;
using System.Text;
using System.Diagnostics;

class Program
{
    static void Main()
    {
        long[] nm = Console.ReadLine().Split().Select(long.Parse).ToArray();
        long n = nm[0];
        long m = nm[1];

        long[] a = new long[m];
        long[] b = new long[m];

        List<long> previouslist = new List<long>();
        List<long> nextlist = new List<long>();

        for (long i = 0; i < m; i++)
        {
            string[] s = Console.ReadLine().Split();
            a[i] = long.Parse(s[0]);
            b[i] = long.Parse(s[1]);


            if(b[i] == n)
            {
                nextlist.Add(a[i]);
            }

            if(a[i] == 1)
            {
                previouslist.Add(b[i]);
            }
        }

        foreach(long item in previouslist)
        {
            if (nextlist.Contains(item))
            {
                Console.WriteLine("POSSIBLE");
                return;
            }
        }
        Console.WriteLine("IMPOSSIBLE");
    }
}