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>
#include<stdlib.h>

typedef struct{
	int p;
	int q;
} ship;

int comp(const void *p1,const void *p2);

int main(void){
	int i,j;
	ship *map;
	int *index;
	int n,m,tmp,flg=0;
	scanf("%d%d",&n,&m);
	map=(ship *)calloc(m,sizeof(ship));
	index=(int*)calloc(n+1,sizeof(int));
	for(i=0;i<m;i++){
		scanf("%d%d",&map[i].p,&map[i].q);
	}
	
	qsort(map,m,sizeof(ship),comp);
	
	//for(i=0;i<m;i++) printf("%d %d\n",map[i].p,map[i].q);
	tmp=0;
	for(i=0;i<=n;i++) index[i]=0;
	for(i=0;i<m;i++){
		if(map[i].p>tmp){
			tmp=map[i].p;
			index[map[i].p]=i;
		}
	}
	index[n]=m;
	
	for(i=1;i<=n;i++){
		//printf("%d%c",index[i],(i==n)?'\n':' ');
	}
	for(i=0;i<index[2];i++){
		for(j=index[map[i].q];map[j].p!=map[i].q;j++){
			//printf("%d %d -> %d\n",i,j,map[j].q);
			if(map[j].q==n){
				flg=1;
				break;
			}
		}
		if(flg==1) break;
	}
	
	if(flg==1) puts("POSSIBLE");
	else puts("IMPOSSIBLE");
	free(map);
	return 0;
}

int comp(const void *p1,const void *p2){
	const ship *d1,*d2;
	d1=(const ship *)p1;
	d2=(const ship *)p2;
	if(d1->p==d2->p) return d1->q-d2->q;
	else return d1->p-d2->p;
}