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++14 (GCC 5.4.1) (judge verdict: Time Limit Exceeded)

#include<stdio.h>
#include <stdlib.h>
int main(void){
long *x,*y,*z;
long N,M,i;
int check = 0,breakflag=0;
int a=0,b=0;
scanf("%ld %ld",&N,&M);
x = (long *)malloc(M*sizeof(long));
y = (long *)malloc(M*sizeof(long));
z = (long *)malloc(M*sizeof(long));
for(i=0;i<M;i++){
scanf("%ld %ld",&x[i],&y[i]);
if(y[i]==N){
z[a]=x[i];
a=a+1;
}
}
for(i=0;i<M;i++){
for(b=0;b<a;b++){
if(x[i]==1 && y[i]==z[b]){
check = 1;
breakflag=1;
break;
}
if(breakflag)break;
}
}
if(check) printf("POSSIBLE");
if(check == 0) printf("IMPOSSIBLE");
free(x);
free(y);

return 0;
}