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>
#include<string.h>

typedef struct{
	int from;
	int to;
}fromTo;

int main(int argc, char *argv[]){

	char line[256];
	int a, b;
	int wantToGo;

	fgets(line, sizeof(line), stdin);
	sscanf(line, "%d %d", &a, &b);
	wantToGo = a;

	fromTo bin[b];
	int max = b;

	int i = 0;
	while(1){
		fgets(line, sizeof(line), stdin);

		if(line[0] == '\n')
			break;
			
		sscanf(line, "%d %d", &a, &b);
		
		bin[i].from = a;
		bin[i].to = b;
		i++;
	}

	i = 0;
	int j = 0;
	int chance = 2;
	while(i < max){

		if(bin[i].from == 1){
			//printf("*** %d\n", bin[i].to);
			if(bin[i].to == wantToGo)
				break;
			else{
				j = 0;
				while(j < max){
					if(bin[j].from == bin[i].to){
						if(bin[j].to == wantToGo)
							goto yes;
					}
					j++;
				}
			}
		}
		i++;
	}

yes:

	if(chance != 0)
		printf("POSSIBLE\n");
	else
		printf("IMPOSSIBLE\n");

	return 0;
}