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: Wrong Answer)

#include <stdio.h>

int enque(int *queue, int data, int *head, int *tail, size_t n) {
    if (*head % n != (*tail + 1) % n) {
        queue[(*tail)++ % n] = data;
        return *tail - *head;
    } else {
        return 0;
    }
}

int deque(int *queue, int *head, int *tail, size_t n) {
    if (*head != *tail) {
        return queue[(*head)++ % n];
    } else {
        return 0;
    }
}

int main(void)
{
	int n,m,head=0,tail=0,tmp,pos=0,pos1=0,pos2=0;
	scanf("%d %d\n",&n,&m);
	int tmpa,tmpb;
	int que1[n],que2[n];
	pos = 0;
	for(int i=0;i<m;++i)
	{
		scanf("%d %d \n",&tmpa,&tmpb);
		if(tmpa==1) {
			enque(que1,tmpb,&tail,&head,n);
			pos1=1;
		}
  	if(tmpb==n) {
  		enque(que2,tmpa,&tail,&head,n);
  		pos2=1;
  	}
	}
	if(pos1==0||pos2==0) {
		puts("IMPOSSIBLE");
		return 0;
  }
  for(int i=0;i<n;++i)
  {
  	tmpa=que1[i];
  	for(int j=0;j<n;++j)
  	{
  		if(que2[j]==tmpa){
  			puts("POSSIBLE");
  			return 0;
  		}
  	}
  }
	puts("IMPOSSIBLE");
	return 0;	
}