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.Linq;
using System.Collections.Generic;

class P
{
    static void Main()
    {
        int[] NM = Console.ReadLine().Split().Select(int.Parse).ToArray();
        List<int> from1Ship = new List<int>();
        List<int> toNShip = new List<int>();
        for (int i = 0; i < NM[1]; i++)
        {
            int[] a = Console.ReadLine().Split().Select(int.Parse).ToArray();
            if (a[0] == 1) from1Ship.Add(a[1]);
            if (a[1] == NM[0]) toNShip.Add(a[0]);
        }
        int[] f1 = from1Ship.OrderBy(x => x).ToArray();
        int[] tN = toNShip.OrderBy(x => x).ToArray();
        int f1index = 0;
        int tnindex = 0;
        while (f1index < f1.Length && tnindex < tN.Length)
        {
            if (f1[f1index] < tN[tnindex]) f1index++;
            else if (f1[f1index] > tN[tnindex]) tnindex++;
            else
            {
                Console.WriteLine("POSSIBLE");
                return;
            }
        }
        Console.WriteLine("IMPOSSIBLE");
    }
}