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;
class Program
{
    static void Main(string[] args)
    {
            // 入力
            string[] sS = Console.ReadLine().Trim().Split(' ');
            int iN = int.Parse(sS[0]);
            int iM = int.Parse(sS[1]);
            List<int> lstFrm1 = new List<int>();        // 1から行ける島
            List<int> lstDesN = new List<int>();        // N  に行ける島
            for (int i = 0; i < iM; i++)
            {
                sS = Console.ReadLine().Trim().Split(' ');
                int ia = int.Parse(sS[0]);
                int ib = int.Parse(sS[1]);
                if (ia == 01) { lstFrm1.Add(ib); }
                if (ib == 01) { lstFrm1.Add(ia); }
                if (ia == iN) { lstDesN.Add(ib); }
                if (ib == iN) { lstDesN.Add(ia); }
            }

            System.Diagnostics.Stopwatch sw = new System.Diagnostics.Stopwatch();
            sw.Start();

            // 解析
            string sOut = "IMPOSSIBLE";
            for (int i = 0; i < lstFrm1.Count; i++)
            {
                if (lstDesN.Contains(lstFrm1[i])) { sOut = "POSSIBLE"; break; }
            }

            //出力
            Console.WriteLine("{0}", sOut.ToString().Trim());

            sw.Stop();
#if DEBUG
            Console.WriteLine();
            Console.WriteLine("{0}", sw.Elapsed.ToString());
            Console.WriteLine("続行するには何かキーを押してください．．．");
            Console.ReadKey();
#endif
    }
}