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 Java8 (OpenJDK 1.8.0) (judge verdict: Runtime Error)

import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.StringTokenizer;

public class Main {

  public static void main(String[] args) throws IOException {
    BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
    int target, num;
    String str = br.readLine();
    StringTokenizer st = new StringTokenizer(str);
    target = Integer.parseInt(st.nextToken());
    num = Integer.parseInt(st.nextToken());

    boolean[] to = new boolean[200000];
    boolean[] from = new boolean[200000];

    for (int i = 0; i < num; i++) {
      str = br.readLine();
      st = new StringTokenizer(str);
      to[Integer.parseInt(st.nextToken())] = true;
      from[Integer.parseInt(st.nextToken())] = true;
    }

    boolean flag = false;
    for (int i = 0; i < 200000 && flag == false; i++) {
      for (int j = 0; j < 200000 && flag == false; j++) {
        if (to[i] == true && from[j] == true) {
          System.out.println("POSSIBLE");
          flag = true;
          break;
        }
      }
    }

    if (!flag) {
      System.out.println("IMPOSSIBLE");
    }
  }

}