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: Accepted)

#include <stdio.h>
#include <stdlib.h>
#include <math.h>
#include <string.h>
#define Rep(i,a,n)for(int i=(int)(a);i<(int)(n);i++)
#define rep(i,n)Rep(i,0,n)
typedef long long ll;
typedef long double ld;

int sort1(const void* a, const void* b) {
	return *(int*)b - *(int*)a;
}

int main() {
	int n, m, a[200001], b[200001], c[200001] = { 0 }, d[200001] = { 0 };
	scanf("%d %d", &n, &m);
	rep(i, m) {
		scanf("%d %d", &a[i], &b[i]);
		if (a[i] == 1)c[b[i]] = 1;
		if (b[i] == n)d[a[i]] = 1;
	}
	rep(i, n) {
		if (c[i] == d[i] && c[i] == 1) { printf("POSSIBLE"); return 0; }
	}
	printf("IMPOSSIBLE");
}