Score : $300$ points
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.
Input is given from Standard Input in the following format:
$N$ $M$ $a_1$ $b_1$ $a_2$ $b_2$ : $a_M$ $b_M$
If it is possible to go to Island $N$ by using two boat services, print
POSSIBLE; otherwise, print
3 2 1 2 2 3
4 3 1 2 2 3 3 4
You have to use three boat services to get to Island $4$.
100000 1 1 99999
5 5 1 3 4 5 2 3 2 4 1 4
You can get to Island $5$ by using two boat services: Island $1$ -> Island $4$ -> Island $5$.