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: Runtime Error)

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

class Program {
    static void Main(string[] args) {
        int n = Cin.Ni();
        int m = Cin.Ni();
        HashSet<int> startSet = new HashSet<int>();
        HashSet<int> goalSet = new HashSet<int>();
        for (int i = 0; i < n; i++) {
            int a = Cin.Ni();
            int b = Cin.Ni();
            if (a == 1) {
                startSet.Add(b);
            }
            if (b == n) {
                goalSet.Add(a);
            }
        }
        startSet.IntersectWith(goalSet);
        Console.WriteLine(startSet.Any() ? "POSSIBLE" : "IMPOSSIBLE");
    }
}


public class Cin {
    private static string[] s = new string[0];
    private static int i = 0;

    private static char[] cs = new char[] { ' ' };

    public static string Next() {
        if (i < s.Length) return s[i++];
        string st = Console.ReadLine();
        while (st == "") st = Console.ReadLine();
        s = st.Split(cs, StringSplitOptions.RemoveEmptyEntries);
        i = 0;
        return Next();
    }

    public static int Ni() {
        return int.Parse(Next());
    }

    public static long NextLong() {
        return long.Parse(Next());
    }

    public static double NextDouble() {
        return double.Parse(Next());
    }

}