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# (.NET Core 3.1.201) (judge verdict: Accepted)

using System;
using System.Linq;
using System.Collections.Generic;

namespace ABC
{
    class ProgramC
    {
        static List<int>[] _list;
        static int _n;
        static int _m;

        static void Main(string[] args)
        {
            var inputs = Console.ReadLine().Split(" ");
            _n = int.Parse(inputs[0]);
            _m = int.Parse(inputs[1]);

            _list = new List<int>[_n];
            for (var i = 0; i < _n; i++)
            {
                _list[i] = new List<int>();
            }

            for (var i = 0; i < _m; i++)
            {
                var inputs1 = Console.ReadLine().Split(" ");
                var a = int.Parse(inputs1[0]) - 1;
                var b = int.Parse(inputs1[1]) - 1;
                _list[a].Add(b);
            }

            var result = dfs(0, 0) ? "POSSIBLE" : "IMPOSSIBLE";
            Console.WriteLine(result);
        }

        static bool dfs(int v, int count)
        {
            if (count == 2)
            {
                return v == _n - 1;
            }

            foreach (var l in _list[v])
            {
                var b = dfs(l, count + 1);
                if (b)
                    return true;
            }

            return false;
        }
    }
}