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: Time Limit Exceeded)

#include <stdio.h>

int main(void)
{
	int n, m;
	scanf("%d %d", &n, &m);

	int *found_ap = malloc(sizeof(int) *m), *found_bp = malloc(sizeof(int) * m);
	size_t found_size = 0;


	int *ap = malloc(sizeof(int) * m);
	int *bp = malloc(sizeof(int) * m);

	for (int i = 0; i < m; i++) {
		scanf("%d %d", &ap[i], &bp[i]);
	}

	int *p = malloc(sizeof(int) * m);
	size_t p_size = 0;

	for (int i = 0; i < m; i++) {
		if (ap[i] == 1 || bp[i] == 1) {
			found_size++;
			//found_ap = realloc(found_ap, sizeof(int) * found_size);
			//found_bp = realloc(found_bp, sizeof(int) * found_size);
			found_ap[found_size-1] = ap[i];
			found_bp[found_size-1] = bp[i];
		}
		if (ap[i] == n) {
			p_size++;
			//p = realloc(p, sizeof(int) * p_size);
			p[p_size-1] = bp[i];
		}

		if (bp[i] == n) {
			p_size++;
			//p = realloc(p, sizeof(int) * p_size);
			p[p_size-1] = ap[i];
		}
	}

	if (p_size == 0) {
		puts("IMPOSSIBLE");
		return 0;
	}



	for (int pp = 0; pp < p_size; pp++) {
		for (int i = 0; i < found_size; i++) {
			if (found_ap[i] == p[pp] || found_bp[i] == p[pp]) {
				puts("POSSIBLE");
				return 0;
			}
		}
	}

	puts("IMPOSSIBLE");
	return 0;
}