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;
using static System.Console;
namespace AtCoder.ARC079
{
    class CatSnukeAndAVoyage
    {
        public static void Main()
        {
            var nm = ReadLine().Trim().Split(' ').Select(_ => int.Parse(_));
            var n = nm.First(); var m = nm.Last();
            var lands = new int[n];
            foreach(var bridge in (new int[m]).Select(_ => ReadLine().Trim().Split(' ').Select(s => int.Parse(s)).OrderBy(num => num))) {
                if (bridge.First() == 1) lands[bridge.Last()] += 1;
                if (bridge.Last() == n) lands[bridge.First()] += n;
            }
            var possible = "POSSIBLE";
            var impossible = "IMPOSSIBLE";
            if (lands.Any(_ => _ == n + 1)) WriteLine(possible);
            else WriteLine(impossible);
        }

    }
}