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>

int tree[200005];

int root(int a)
{
	if (tree[a] < 0) {
		return a;
	} else {
		tree[a] = root(tree[a]);
	}
}

int same(int a, int b)
{
	a = root(a);
	b = root(b);

	return a == b;
}


void unite(int a, int b)
{
	a = root(a);
	b = root(b);

	if (!same(a, b)) {
		tree[a] += tree[b];
		tree[b] = a;
	}
	
	return;
}

int main()
{
	int n, m;
	int a, b;

	for (int i = 0; i <= 200000; i++) {
		tree[i] = -1;
	}

	scanf("%d %d", &n, &m);
	for (int i = 0; i < m; i++) {
		scanf("%d %d", &a, &b);
		
		if (a == 1) {
			unite(a, b);
		} else if (b == n) {
			unite(a, b);
		}
	}

	if (same(1, n)) {
		puts("POSSIBLE");
	} else {
		puts("IMPOSSIBLE");
	}

	return 0;
}