Missing order numbers

Problem

Orders are numbered 1 to N. The warehouse received some of the numbers (a number may be received twice). Find the numbers that never arrived.

Input: The first line has N and k. The second line has k received numbers (k can be 0, then the line is empty).
Output: The missing numbers in ascending order on one line, separated by spaces, or NONE if no number is missing.
Constraints: 1 ≤ N ≤ 10^5
0 ≤ k ≤ 2 × 10^5
Each received number is between 1 and N

Example

Input

8 6
3 1 7 3 5 8

Output

2 4 6

2, 4 and 6 never arrived.

Try the problem first. Open one hint at a time.

Hint 1

Put the received numbers in a HashSet<Integer>.

Hint 2

Loop i from 1 to N and collect the numbers the set does not contain.

Write your Java code, run it on the examples and submit it to hidden tests.