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 Ruby (2.3.3) (judge verdict: Time Limit Exceeded)

require 'set'

n , m = gets.split(" ").map(&:to_i)

map = Hash.new { |h, k| h[k] = [] }

m.times do
  a , b = gets.split(" ").map(&:to_i)
  map[a] << b
  map[b] << a
end

q = Set.new([*1..n])
d = {}
d[1] = 0
routes = {}

until q.empty?
  u = d.keys.select { |k| q.include? k }.min_by { |k| d[k] }
  q.delete(u)

  break if u.nil?

  map[u].each do |v|
    if d.key?(u) || (d[u] + 1 < d[v])
      d[v] = d[u] + 1
      routes[v] = u
    end
  end
end

prev = 1
cnt = 0

while cnt < 2
  prev = routes[prev]
  cnt += 1
  break if prev == n
end

puts prev == n ? "POSSIBLE" : "IMPOSSIBLE"