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 (GCC 5.4.1) (judge verdict: Runtime Error)

#include <stdio.h>

struct ship {
	int from;
	int to;
};

int main()
{
	int n;
	int m;
	int i;
	int j;
	int is_ok = 0;
	struct ship table[20000] = { 0 };
	
	if (scanf("%d %d", &n, &m) == EOF) {
		goto end;
	}
	
	for (i = 0; i < m; i++) {
		if (scanf("%d %d", &table[i].from, &table[i].to) == EOF) {
			goto end;
		}
	}
	
	for (i = 0; i < m; i++) {
		if (table[i].from != 1) {
			continue;
		}
		for(j = 0; j < m; j++){
			if (table[j].from == table[i].to && table[j].to == n) {
				is_ok++;
				break;
			}
		}
	}
	
	if (is_ok) {
		printf("POSSHIBLE\n");
	} else {
		printf("IMPOSSHIBLE\n");
	}

end:
	return 0;
}