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 ConsoleApp106 {
    class Program {
        static void Main(string[] args) {
            var st = Console.ReadLine().Split().Select(int.Parse).ToArray();

            int N = st[0];
            int M = st[1];

            var a = new int[M];
            var b = new int[M];

            var tupleList = new List<Tuple<int, int>>();

            var candList = new List<int>();

            for (int i = 0; i < M; i++) {
                var x = Console.ReadLine().Split().Select(int.Parse).ToArray();

                a[i] = Math.Min(x[0], x[1]);
                b[i] = Math.Max(x[0], x[1]);

                tupleList.Add(new Tuple<int, int>(a[i], b[i]));

                if (b[i] == N) {
                    candList.Add(a[i]);
                }
            }

            if (tupleList.Count() == 0) {
                Console.WriteLine("IMPOSSIBLE");
                return;
            }

            foreach(var element in candList) {
                if (tupleList.Contains(new Tuple<int, int>(1, element))) {
                    Console.WriteLine("POSSIBLE");
                    return;
                }
            }

            Console.WriteLine("IMPOSSIBLE");


        }
    }
}