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 Python (3.4.3) (judge verdict: Time Limit Exceeded)

n, m = map(int, input().split())
hunes = []
for i in range(m):
  hunes.append(list(map(int,input().split())))

hune1 = []
hune2 = []
for keiro in hunes:
  keiro.sort()
  if keiro[0] == 1:
    hune1.append(keiro)
  if keiro[1] == n:
    hune2.append(keiro)

tohune1 = []
for to in hune1:
  tohune1.append(to[1])

fromhune2 = []
for fom in hune2:
  fromhune2.append(fom[0])

ikeru = []
for to in tohune1:
  for fom in fromhune2:
    if to == fom:
      print("POSSIBLE")
      ikeru.append(1)
if len(ikeru) == 0:
  print("IMPOSSIBLE")