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;

class Program
{
    static string InputPattern = "InputX";

    static List<string> GetInputList()
    {
        var WillReturn = new List<string>();

        if (InputPattern == "Input1") {
            WillReturn.Add("3 2");
            WillReturn.Add("1 2");
            WillReturn.Add("2 3");
            //POSSIBLE
        }
        else if (InputPattern == "Input2") {
            WillReturn.Add("4 3");
            WillReturn.Add("1 2");
            WillReturn.Add("2 3");
            WillReturn.Add("3 4");
            //IMPOSSIBLE
        }
        else if (InputPattern == "Input3") {
            WillReturn.Add("100000 1");
            WillReturn.Add("1 99999");
            //IMPOSSIBLE
        }
        else if (InputPattern == "Input4") {
            WillReturn.Add("5 5");
            WillReturn.Add("1 3");
            WillReturn.Add("4 5");
            WillReturn.Add("2 3");
            WillReturn.Add("2 4");
            WillReturn.Add("1 4");
            //POSSIBLE
        }
        else {
            string wkStr;
            while ((wkStr = Console.ReadLine()) != null) WillReturn.Add(wkStr);
        }
        return WillReturn;
    }

    static void Main()
    {
        List<string> InputList = GetInputList();

        int[] wkArr = { };
        Action<string> SplitAct = pStr =>
            wkArr = pStr.Split(' ').Select(X => int.Parse(X)).ToArray();
        SplitAct(InputList[0]);
        int N = wkArr[0];

        var ZenhanSet = new HashSet<int>();
        var KouhanSet = new HashSet<int>();

        foreach (string EachStr in InputList.Skip(1)) {
            SplitAct(EachStr);
            int A = wkArr[0];
            int B = wkArr[1];

            if (A == 1) {
                ZenhanSet.Add(B);
            }
            if (B == N) {
                KouhanSet.Add(A);
            }
        }
        ZenhanSet.IntersectWith(KouhanSet);

        if (ZenhanSet.Count>0) {
            Console.WriteLine("POSSIBLE");
        }
        else Console.WriteLine("IMPOSSIBLE");
    }
}