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.Linq;
using System.Collections.Generic;

class Cmondai
{
    struct Connection{
        public List<long> list;
        public Connection(int index) {
            list = new List<long>();
        }
    }

    static void Main()
    {
        var nm = Console.ReadLine().Split(' ').Select(x => Int32.Parse(x)).ToArray();
        var N = nm[0];
        var M = nm[1];
        var connection = new Connection[N];
        for (int i = 0; i < N; ++i) connection[i] = new Connection(i);
        for (int i=0;i<M;++i)
        {
            var a = Console.ReadLine().Split(' ').Select(x => Int64.Parse(x)).ToArray();
            connection[a[0] - 1].list.Add(a[1] - 1);
            connection[a[1] - 1].list.Add(a[0] - 1);
        }

        var hashSet = new HashSet<long>();
        Dfs(hashSet, connection, 0,0);
        var ans = "IMPOSSIBLE";
        if (hashSet.Contains(N-1)) ans= "POSSIBLE";

        Console.WriteLine(ans);
    }
    static void Dfs(HashSet<long> hashSet, Connection[] connection, long index,int deep)
    {
        if (2 < deep) return;
        hashSet.Add(index);
        foreach (var l in connection[index].list)
        {
            deep = index == 0 ? 0 : deep;
            Dfs(hashSet, connection, l,++deep);
        }
    }
}