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;
using static System.Console;
using static System.Convert;
using static System.Math;

class Program
{
    class P
    {
        public int index;
        public List<int> ad;
        public P(int index)
        {
            this.index = index;
            ad = new List<int>();
        }
    }
    static void Main(string[] args)
    {
        var nm = Array.ConvertAll(ReadLine().Split(' '), int.Parse);
        var ps = new P[nm[0]];
        for (var i = 0; i < nm[0]; i++)
            ps[i] = new P(i);
        for(var i = 0; i < nm[1]; i++)
        {
            var input = Array.ConvertAll(ReadLine().Split(' '), int.Parse);
            ps[input[0] - 1].ad.Add(input[1] - 1);
        }
        var isGoal = false;
        dfs(ps, nm[0], 0, 0,ref isGoal, new HashSet<int>());
        WriteLine(isGoal ? "POSSIBLE" : "IMPOSSIBLE");
    }
    private static void dfs(P[] ps,int num,int index,int depth,ref bool isGoal,HashSet<int> set)
    {
        if (index == num - 1) { isGoal = true; return; }
        else if (depth == 2) return;

        foreach(var p in ps[index].ad)
        {
            if (!set.Contains(p) && !isGoal)
                dfs(ps, num, p, depth+1,ref isGoal, set);
        }
    }
    private const string ALFA = "abcdefghijklmnopqrstuvwxyz";
    private const int MOD = 1000000007;
}