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 'pp'

# 空白区切の入力値を数値の配列で返却する
def gets_i_list()
  gets.chomp.split(" ").map(&:to_i)
end

# 有向グラフ
# { 0 => [0,1,2,3,4,], 1 => [0,1,2,3,4,], ...}
def createDirectedGraph(from_to_list)
  graph = Hash.new{[]}
  from_to_list.each do |from, to|
    to_list = graph[from]
    to_list.push(to)
    graph[from] = to_list.sort
  end
  graph
end

N, M = gets_i_list
ab_list = M.times.map do
  gets_i_list
end

graph = createDirectedGraph(ab_list)
e2 = graph[1]
e2.each do |from|
  e3 = graph[from]
  if e3.include?(N)
    puts "POSSIBLE"
    exit
  end
end
puts "IMPOSSIBLE"