Nevest has a sequence A with N distinct elements. She wants to have a sequence S with length M and all of the conditions below must be fulfilled:

• For all subarrays in S of length K, the sum of each number in the subarray must be divisible by K.
• For 1 ≤ i < j ≤ M, S_i ≠ S_j must hold.
• A must be a subsequence of S.
• For 1 ≤ i ≤ M, constrain 1 ≤ S_i ≤ 5 × 10⁵ must be fulfilled.
• The length of sequence S mustn't exceed 5 × 10⁵.

Nevest is not very good at problem-solving so she asked you instead. Help Nevest by giving her any valid sequence or print "-1" if no valid sequence exist (without quotation marks).

Please note that you don't have to minimize M.

Input Format

N K
A₁ A₂ ... A_N

Output Format

If there's a valid answer, print M in the first line followed by a line containing sequence S with M numbers. If there's no valid sequence S print "-1" (without quotation marks).

Sample Input 1

5 3
1 3 2 5 4

Sample Output 1

7
1 3 2 7 9 5 4

Sample Input 2

4 2
1 3 5 7

Sample Output 2

4
1 3 5 7

Constraints

• 1 ≤ K ≤ N ≤ 500
• 1 ≤ A_i ≤ 500
• A_i ≠ A_j, for 1 ≤ i < j ≤ N