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>
#define MAX_NUM 200000
#define BIRTHDAY 1009

typedef struct hash{
	int num;
	struct hash *next;
}hash;

void append(hash**, int);
void search(hash**, int);
void possible();

int a_list[MAX_NUM] = {0};
int a_index = 0;
hash *hash_list[MAX_NUM/BIRTHDAY + 1] = {NULL};

int main(void){
	int N, M;
	int a, b;
	int i;
	hash *p;

	scanf("%d %d", &N, &M);
	for(i = 0; i < M; i++){
		scanf("%d %d", &a, &b);
		if(a == 1){
			append(hash_list, b);
		}
		if(b == N){
			a_list[a_index++] = a;
		}
	}

	for(i=0; i<a_index; i++){
		search(hash_list, a_list[i]);
	}

	printf("IMPOSSIBLE");
	return 0;
}

void append(hash **list, int num){
	hash *p, *tmp;
	hash *item;
	tmp = NULL;
	for(p = list[num%BIRTHDAY]; p != NULL && p->num < num; p = p->next)
		tmp = p;

	item = (hash*)malloc(sizeof(hash));
	item->num = num;
	item->next = p;
	if(tmp == NULL)
		list[num%BIRTHDAY] = item;
	else
		tmp->next = item;
}

void search(hash **list, int num){
	hash *p;
	for(p = list[num%BIRTHDAY]; p != NULL && p->num <= num; p = p->next){
		if(p->num == num)
			possible();
	}
}

void possible(){
	printf("POSSIBLE");
	exit(1);
}