Problem:
Score : 500 points

Problem Statement

Given are N integers A_1,\ldots,A_N.

We will choose exactly K of these elements. Find the maximum possible product of the chosen elements.

Then, print the maximum product modulo (10^9+7), using an integer between 0 and 10^9+6 (inclusive).

Constraints

1 \leq K \leq N \leq 2\times 10^5

|A_i| \leq 10^9

Input

Input is given from Standard Input in the following format:

N K
A_1 \ldots A_N

Output

Print the maximum product modulo (10^9+7), using an integer between 0 and 10^9+6 (inclusive).

Sample Input 1

4 2
1 2 -3 -4

Sample Output 1

12

The possible products of the two chosen elements are 2, -3, -4, -6, -8, and 12, so the maximum product is 12.

Sample Input 2

4 3
-1 -2 -3 -4

Sample Output 2

1000000001

The possible products of the three chosen elements are -24, -12, -8, and -6, so the maximum product is -6.

We print this value modulo (10^9+7), that is, 1000000001.

Sample Input 3

2 1
-1 1000000000

Sample Output 3

1000000000

The possible products of the one chosen element are -1 and 1000000000, so the maximum product is 1000000000.

Sample Input 4

10 10
1000000000 100000000 10000000 1000000 100000 10000 1000 100 10 1

Sample Output 4

999983200

Be sure to print the product modulo (10^9+7).

Solution in Common Lisp (SBCL 2.0.3) (judge verdict: Runtime Error)

(let* ((n (read))
       (k (read))
       (a (make-array (list n)))
       (l 0)
       (mn 0)
       (r (1- n))
       (ans 1)
       (b (+ (expt 10 9) 7)))
  (defun mod-* (x y)
    (mod (* x y) b))
  ;
  (loop :for i :from 0 :to (1- n)
        :do (let ((x (read)))
              (if (< x 0) (incf mn))
              (setf (aref a i) x)))
  (setf a (sort a #'>))
  (if (and (= mn n) (oddp k))
      (loop :for j :form 1 :to n
            :for i :from (1- n)
            :do (setf ans (mod-* ans (aref a i))))
      ;;
      (loop :while (< (+ l (- n 1 r)) k)
            :if (and (< (aref a l) (* (aref a r) (aref a (1- r)))) (>= (- k 2) (+ l (- n 1 r))) (>= (aref a l) 0))
            :do (progn
                  (setf ans (mod-* ans (mod-* (aref a r) (aref a (1- r)))))
                  (decf r 2))
            :else
            :do (progn
                  (setf ans (mod-* ans (aref a l)))
                  (incf l))))
  (format t "~A~%" ans))