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;

namespace AtCoder
{
    class Program
    {
        static void Main(string[] args)
        {
            string[] str1 = Console.ReadLine().Split(' ');
            int 島の数 = int.Parse(str1[0]);
            int 定期便の数 = int.Parse(str1[1]);

            List<int> list1 = new List<int>();
            List<int> listN = new List<int>();

            string[] str2;
            int from, to;
            for (int i = 0; i < 定期便の数; i++)
            {
                str2 = Console.ReadLine().Split(' ');
                from = int.Parse(str2[0]);
                to = int.Parse(str2[1]);

                if(from == 1 && to == 島の数)
                {
                    Console.WriteLine("POSSIBLE");
                    return;
                }
                else if(from == 1)
                {
                    list1.Add(to);
                }
                else if(to == 島の数)
                {
                    if(list1.Contains(to))
                    {
                        Console.WriteLine("POSSIBLE");
                        return;
                    }
                    listN.Add(from);
                }
            }

            foreach(var a in list1)
            {
                foreach(var b in listN)
                {
                    if(a == b)
                    {
                        Console.WriteLine("POSSIBLE");
                        return;
                    }
                }
            }
            Console.WriteLine("IMPOSSIBLE");
            return;
            
        }
    }
}