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 CSharpConsoleApp {

    public class Hen {
        public int start;
        public int end;

    }

    class Program {

        static int Main() {
            var HenArray = new List<Hen>();
            var target = Console.ReadLine().Split(' ').Select(s => int.Parse(s)).ToArray();
            var goal = target[0];
            for (int i = 0; i < target[1]; i++) {
                var input = Console.ReadLine().Split(' ').Select(s => int.Parse(s)).ToArray();
                Hen hen = new Hen() {
                    start = input[0],
                    end = input[1]
                };
             //   if (hen.end < goal)
                    HenArray.Add(hen);
            }
            bool isSucceed = false;
            var firstGoal = HenArray.Where(h => h.start == 1&& h.end !=goal).Select(h => h.end).ToList();
            foreach (var s in firstGoal) {
                if (HenArray.Where(h => h.start == s).Any(h => h.end == goal)) {
                    isSucceed = true;
                    break;
                }
            }
            if (isSucceed)
                Console.WriteLine("POSSIBLE");
            else
                Console.WriteLine("IMPOSSIBLE");
            return 0;
        }
    }
}