voyage2
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 ai and Island bi.
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 ≤ ai < bi ≤ N
- (ai, bi) ≠ (1, N)
- If i ≠ j, (ai, bi) ≠ (aj, bj).
Input
Input is given from Standard Input in the following format:
N M
a1 b1
a2 b2
:
aM bM
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.