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: Time Limit Exceeded)

#include <stdio.h>
#include <stdlib.h>
#define MAX_NUM 200000

int int_sort(const void *a, const void *b) {
  if(*(int*)a < *(int*)b){
    return -1;
  }else if(*(int*)a == *(int*)b){
    return 0;
  }
  return 1;
}

int main(void){
	int N, M;
	int i, j;
	int a, b;
	int first[MAX_NUM] = {0};
	int second[MAX_NUM] = {0};
	int first_index, second_index;

	scanf("%d %d", &N, &M);
	first_index = 0; second_index = 0;
	for(i=0; i<M; i++){
		scanf("%d %d", &a, &b);
		if(a == 1)
			first[first_index++] = b;
		if(b == N)
			second[second_index++] = a;
	}

	qsort((void*)first, first_index, sizeof(first[0]), int_sort);
	qsort((void*)second, second_index, sizeof(second[0]), int_sort);

	/*puts("first:");
	for(i=0; i<first_index; i++){
		printf("first[%d]: %d\n", i, first[i]);
	}
	putchar('\n');
	puts("second:");
	for(i=0; i<second_index; i++){
		printf("second[%d]: %d\n", i, second[i]);
	}*/

	for(i=0; i<first_index; i++){
		for(j=0; j<second_index; j++){
			if(second[j] > first[i])
				break;
			if(first[i] == second[j]){
				printf("POSSIBLE");
				return 0;
			}
		}
	}

	printf("IMPOSSIBLE");
	return 0;
}