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: Time Limit Exceeded)


import java.util.Scanner;

public class Main {

	public static void main(String[] args) {

		try (Scanner s = new Scanner(System.in)) {
			final int N = s.nextInt();
			final int M = s.nextInt();
			
			// 経路入力
			int[] a = new int[M];
			int[] b = new int[M];
			for (int i = 0; i < M; i++) {
				a[i] = s.nextInt();
				b[i] = s.nextInt();
			}
			
			search(N, M, a, b, 2);
			System.out.println("IMPOSSIBLE");
		}
	}
	
	private static void search(int N, int M, int[] a, int[] b, int lim) {
		if (lim == 0 && N == 1) {
			System.out.println("POSSIBLE");
			System.exit(0);
		}
		
		for (int i = 0; i < M; i++) {
			if (b[i] == N) {
				search(a[i], M, a, b, lim - 1);
			}
		}
	}
}