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 Julia (0.5.0) (judge verdict: Time Limit Exceeded)

function main()
  
  (N, M) = map(x -> parse(Int, x), split(readline()))

  check_1 = zeros(Int, N)
  check_N = zeros(Int, N)
  
  for i in 1:M
    (a, b) = map(x -> parse(Int, x), split(readline()))
    if a == 1
      check_1[b] = 1
    elseif b == 1
      check_1[a] = 1
    elseif b == N
      check_N[a] = 1
    elseif a == N
      check_N[b] = 1
    end
  end
  
  ans = false
  
  for i in 1:N
    if check_1[i] ==  check_N[i] == 1
      ans = true
      break
    end
  end  
  
  if ans
    println("POSSIBLE")
  else
    println("IMPOSSIBLE")
  end
  
end

main()