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;
using static System.Math;

class Program{
  public static void Main(){

    var input = Console.ReadLine().Split();
    int n = int.Parse(input[0]);
    int m = int.Parse(input[1]);
    var graph = new bool[n+1,n+1];

    for(int i=0; i<m; i++){
      var input2 = Console.ReadLine().Split();
      int a = int.Parse(input2[0]);
      int b = int.Parse(input2[1]);
      graph[a-1,b-1] = true;
      graph[b-1,a-1] = true;
    }
    bool c = false;
    for(int i=0; i<n; i++){
      if(graph[0,i] && graph[i,n-1]){
        c = true;
        break;
      }
    }
    if(c) Console.WriteLine("POSSIBLE");
    else Console.WriteLine("IMPOSSIBLE");
  }
}