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>
#include <string.h>
#include <stdbool.h>
#include <math.h>

/*ソートの時に使う
int sort(const void *a, const void *b){
    return *(int*)a-*(int*)b ;
}
    qsort (data,sizeof(data),sizeof(int),sort); 
*/

int main(void){
    int n,m;
    scanf("%d%d",&n,&m);
    int a[m],b[m],c[m],count=0;
    for (int i=0; i<m; i++){
        scanf("%d%d",&a[i],&b[i]);
        if (a[i]==1){
            c[count]=b[i];
            count++;
        }
        
    }
    for (int i=0; i<m; i++){
        if (b[i]==n){
            for (int j=0; j<count; j++){
                if (a[i]==c[j]){
                    printf("POSSIBLE\n");
                    exit(0);
                }
            }
        }
    }
    printf("IMPOSSIBLE\n");
	return 0 ;
}