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.Collections.Generic;
using System.Diagnostics;
using System.Diagnostics.Contracts;
using System.Linq;

namespace at_coder
{
#if TEST
    [TestClass]
#endif
    public class Test_068_c
    {

#if TEST
        public static void Test_Main()
#else
        public static void Main()
#endif
        {
            int N, M;
            ReadInt(out N, out M);

            List<Ship> ships = new List<Ship>();

            for (int i=0;i<M;i++)
            {
                int f, t;
                ReadInt(out f, out t);
                ships.Add(new Ship(f, t));
            }

            // 到達可能島リスト
            int[] reachable_islands = new int[N];
            for(int i=0;i<N;i++)
            {
                reachable_islands[i] = int.MaxValue;
            }

            // 初期位置は到達可能なのでTrue
            reachable_islands[0] = 0;
            // 探索予定島
            Queue<int> search_list = new Queue<int>();
            
            search_list.Enqueue(0);

            while(search_list.Count > 0)
            {
                int now_island = search_list.Dequeue();
                // 各到達可能な島ごとに移動シミュレーション
                if (reachable_islands[now_island] == int.MaxValue)
                    continue;

                foreach(var ship in ships)
                {
                    // # 現在地の島発の船かつ目標島が到達済みでなければ移動シミュレート実行
                    if (now_island == ship.land_from &&
                        reachable_islands[ship.land_to] > reachable_islands[ship.land_from] + 1)
                    {
                        // 到達済の印をつける
                        reachable_islands[ship.land_to] = reachable_islands[ship.land_from] + 1;
                        // 到着島を探索予定リストに追加
                        if (reachable_islands[ship.land_to] < 3)
                        {
                            search_list.Enqueue(ship.land_to);
                        }
                    }
                }
            }

            // 最後の島が到達可能であるかを判定
            if (reachable_islands[N - 1] == 2)
            {
                Write("POSSIBLE");
            } 
            else
            {
                Write("IMPOSSIBLE");
            }
        }

        public class Ship
        {
            public Ship(int land_from, int land_to)
            {
                this.land_from = land_from - 1;
                this.land_to = land_to - 1;
            }

            public int land_from { get; private set; }
            public int land_to { get; private set; }
        }


        private static void Write(string s)
        {
            Console.WriteLine(s);
        }

        private static int[] ReadIntArray()
        {
            string[] ss = Console.ReadLine().Split(new char[] { ' ' }, StringSplitOptions.RemoveEmptyEntries);
            int[] ar = new int[ss.Length];
            for (int i = 0; i < ss.Length; i++)
            {
                ar[i] = int.Parse(ss[i]);
            }
            return ar;
        }
        private static int ReadInt()
        {
            return int.Parse(Console.ReadLine());
        }
        private static void ReadInt(out int a, out int b)
        {
            var ar = ReadIntArray();
            a = ar[0];
            b = ar[1];
        }
        private static void ReadInt(out int a, out int b, out int c)
        {
            var ar = ReadIntArray();
            a = ar[0];
            b = ar[1];
            c = ar[2];
        }
        private static string ReadString()
        {
            return Console.ReadLine();
        }
        private static string[] ReadStringArray()
        {
            string[] ss = Console.ReadLine().Split(new char[] { ' ' }, StringSplitOptions.RemoveEmptyEntries);
            return ss;
        }
#if !TEST
    }
}
#endif