Contest: Task: Related: TaskB

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.

Help him.

- $3 ≤ N ≤ 200$ $000$
- $1 ≤ M ≤ 200$ $000$
- $1 ≤ a_i < b_i ≤ N$
- $(a_i, b_i) \neq (1, N)$
- If $i \neq j$, $(a_i, b_i) \neq (a_j, b_j)$.

Input 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 `IMPOSSIBLE`

.

3 2 1 2 2 3

POSSIBLE

4 3 1 2 2 3 3 4

IMPOSSIBLE

You have to use three boat services to get to Island $4$.

100000 1 1 99999

IMPOSSIBLE

5 5 1 3 4 5 2 3 2 4 1 4

POSSIBLE

You can get to Island $5$ by using two boat services: Island $1$ -> Island $4$ -> Island $5$.