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.
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.