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 Common Lisp (SBCL 1.1.14) (judge verdict: Time Limit Exceeded)

(declaim (optimize (speed 3) (debug 0) (safety 0)))

(defun find-path (start end path-list cnt)
  (if (and (< cnt 3) (= start end))
      cnt
      (let ((possible-path-list
              (remove-if-not (lambda (path)
                               (= (car path) start))
                             path-list)))
        (mapcar (lambda (path)
                  (find-path (cadr path) end path-list (1+ cnt)))
                possible-path-list))))

(defun reach? (tree)
  (let ((possible? nil))
    (labels ((walk-tree (tree)
               (cond (possible? nil)
                     ((and (numberp tree)
                           (<= tree 2))
                      (setf possible? t))
                     ((consp tree)
                      (walk-tree (car tree))
                      (walk-tree (cdr tree)))
                     ((null tree) nil))))
      (walk-tree tree)
      possible?)))

(let* ((n (read))
       (m (read))
       (path-list (loop repeat m collect (list (read) (read)))))
  (if (reach? (find-path 1 n path-list 0))
      (format t "POSSIBLE~%")
      (format t "IMPOSSIBLE~%")))