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;
class Program
{
    static void Main(string[] args)
    {
        //int[] am = new int[200000];
        //int[] bm = new int[200000];
        // 整数の入力
        string[] input = Console.ReadLine().Split(' ');
        int N = int.Parse(input[0]);
        int M = int.Parse(input[1]);

        int[] cIsland = new int[N+1];
        int chk = 0;
        int k = 0;


        for (int i = 0; i < M; i++) {

            string[] ip = Console.ReadLine().Split(' ');
            int a = int.Parse(ip[0]);
            int b = int.Parse(ip[1]);
            if (a == 1 || b == 1) {
                //cIsland[k] = a + b - 1;
                
                // for (int j = 0; j < k; j++) {
                //     if (cIsland[j] == cIsland[k]){
                //         chk = 1;
                //         break;
                //     }
                // }

                if (cIsland[a + b - 1] ==1){
                    chk = 1;
                        break;
                    }else{
                        cIsland[a + b - 1] =1;
                    }
                k++;
            }

            if (chk == 1)break;

            if (a == N || b == N) {
                //cIsland[k] = a + b - N;
                
                // for (int j = 0; j < k; j++) {
                //     if (cIsland[j] == cIsland[k]){
                //         chk = 1;
                //         break;
                //     }
                // }
                if (cIsland[a + b - N] == 1){
                    chk=1;
                    break;
                    }else{
                        cIsland[a + b - N] = 1;
                    }
                k++;
            }

            if (chk == 1)break;

        }



        if (chk == 0) {
            Console.WriteLine("IMPOSSIBLE");
        } else {
            Console.WriteLine("POSSIBLE");
        }

    }
}