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>

#define NUM 200000

typedef struct{
	int a;
	int b;
}BIN;

int main(void)
{
	int island, bin;
	BIN place;
	int pickup_a[NUM];
	int pickup_b[NUM];
	int i, j, count_a, count_b;
	
	/* ----- input ----- */
	scanf("%d %d", &island, &bin);
	for(count_a=0, count_b=0, i=0; i<bin; i++){
		scanf("%d %d", &place.a, &place.b);
		
		if(place.a == 1)
			pickup_b[count_b++] = place.b;
		if(place.b == island)
			pickup_a[count_a++] = place.a;
	}
	
	/* ----- to_do & output  ----- */
	if(count_a == 0 || count_b == 0){
		printf("IMPOSSIBLE");
		return 0;
	}
	
	for(i=0; i<count_a; i++){
		for(j=0; j<count_b; j++){
			if(pickup_a[i] == pickup_b[j]){
				printf("POSSIBLE");
				return 0;
			}
		}
	}
	
	printf("IMPOSSIBLE");
	
	return 0;
}