Problem Brief

Get Distinct Goodness Values

INTERNNEW GRADOA

A coding competition organized to hire software engineers includes an interesting problem on Bitwise-OR.

The goodness of a sequence is defined as the bitwise-OR of its elements. Given an array arr of length n, find all possible distinct values of goodness that can be obtained by choosing any strictly increasing subsequence of the array. Sort the return array in non-decreasing order.

Note: A subsequence is a sequence that can be derived from the given sequence by deleting zero or more elements without changing the order of the remaining elements.

Function Description

Complete the function getGoodnessValue in the editor.

getGoodnessValue has the following parameters:

int arr[n]: an array of integers

Returns

int[]: all possible distinct values of goodness

🌷 Aura Man the slayer 🙌

1Example 1

Input

arr = [4, 2, 4, 1]

Output

[0, 1, 2, 4, 6]

Explanation

The strictly increasing subsequences which can be choosen to have distinct goodness values are: * Empty subsequence; goodness = 0 * [1]; goodness = 1 * [2]; goodness = 2 * [4]; goodness = 4 * [2, 4]; goodness = 6 There are no other strictly increasing subsequences that yield a different goodness value. So, the answer is [0, 1, 2, 4, 6], which is sorted in non-decreasing order.

2Example 2

Input

arr = [3, 2, 4, 6]

Output

[0, 2, 3, 4, 6, 7]

Explanation

The strictly increasing subsequences which can be choosen to have distinct goodness values are: * Empty subsequence; goodness = 0 * [2]; goodness = 2 * [3]; goodness = 3 * [2, 4]; goodness = 6 * [3, 4]; goodness = 7

3Example 3

Input

arr = [3, 5, 5, 1]

Output

[0, 1, 3, 5, 7]

Explanation

Given n = 4, arr = [3, 5, 5, 1] Strictly increasing subsequences that have distinct goodness values are: Empty subsequence; goodness = 0 [1]; goodness = 1 [3]; goodness = 3 [5]; goodness = 5 [3, 5]; goodness = 7

Constraints

Limits and guarantees your solution can rely on.

1 ≤ n, m ≤ 10^4
1 <= arr[i] < 1024