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 Yorukatsu036.Questions;
using Yorukatsu036.Extensions;
using System;
using System.Collections.Generic;
using System.IO;
using System.Linq;
using System.Text;

namespace Yorukatsu036.Questions
{
    /// <summary>
    /// ABC068 C
    /// </summary>
    public class QuestionC : AtCoderQuestionBase
    {
        List<int>[] ships;

        public override IEnumerable<object> Solve(TextReader inputStream)
        {
            var nm = inputStream.ReadIntArray();
            var islandsCount = nm[0];
            var shipsCount = nm[1];

            ships = Enumerable.Repeat(0, islandsCount).Select(_ => new List<int>()).ToArray();

            for (int i = 0; i < shipsCount; i++)
            {
                var ab = inputStream.ReadIntArray().Select(j => j - 1).ToArray();
                ships[ab[0]].Add(ab[1]);
                ships[ab[1]].Add(ab[0]);
            }

            var distances = GetDistancesFrom(0);

            yield return distances[islandsCount - 1] <= 2 ? "POSSIBLE" : "IMPOSSIBLE";
        }

        int[] GetDistancesFrom(int start)
        {
            var toGo = new Queue<int>();
            toGo.Enqueue(start);
            var distances = Enumerable.Repeat(1 << 28, ships.Length).ToArray();
            distances[0] = 0;

            while (toGo.Any())
            {
                var current = toGo.Dequeue();
                if (distances[current] <= 2)
                {
                    foreach (var island in ships[current])
                    {
                        if (distances[island] > distances[current])
                        {
                            distances[island] = distances[current] + 1;
                            toGo.Enqueue(island);
                        }
                    }
                }
            }

            return distances;
        }
    }
}


namespace Yorukatsu036
{
    class Program
    {
        static void Main(string[] args)
        {
            IAtCoderQuestion question = new QuestionC();    // 問題に合わせて書き換え
            var answers = question.Solve(Console.In);
            foreach (var answer in answers)
            {
                Console.WriteLine(answer);
            }
        }
    }
}

#region Base Classes

namespace Yorukatsu036.Questions
{

    public interface IAtCoderQuestion
    {
        IEnumerable<object> Solve(string input);
        IEnumerable<object> Solve(TextReader inputStream);
    }

    public abstract class AtCoderQuestionBase : IAtCoderQuestion
    {
        public IEnumerable<object> Solve(string input)
        {
            var stream = new MemoryStream(Encoding.Unicode.GetBytes(input));
            var reader = new StreamReader(stream, Encoding.Unicode);

            return Solve(reader);
        }

        public abstract IEnumerable<object> Solve(TextReader inputStream);
    }

}

#endregion

#region Extensions

namespace Yorukatsu036.Extensions
{
    internal static class TextReaderExtensions
    {
        internal static int ReadInt(this TextReader reader) => int.Parse(ReadString(reader));
        internal static long ReadLong(this TextReader reader) => long.Parse(ReadString(reader));
        internal static double ReadDouble(this TextReader reader) => double.Parse(ReadString(reader));
        internal static string ReadString(this TextReader reader) => reader.ReadLine();

        internal static int[] ReadIntArray(this TextReader reader, char separator = ' ') => ReadStringArray(reader, separator).Select(int.Parse).ToArray();
        internal static long[] ReadLongArray(this TextReader reader, char separator = ' ') => ReadStringArray(reader, separator).Select(long.Parse).ToArray();
        internal static double[] ReadDoubleArray(this TextReader reader, char separator = ' ') => ReadStringArray(reader, separator).Select(double.Parse).ToArray();
        internal static string[] ReadStringArray(this TextReader reader, char separator = ' ') => reader.ReadLine().Split(separator);
    }
}

#endregion