Given an integer array `nums` and an integer `k`, modify the array in the following way:

- choose an index `i` and replace `nums[i]` with `-nums[i]`.

You should apply this process exactly `k` times. You may choose the same index `i` multiple times.

Return the largest possible sum of the array after modifying it in this way.

Example 1:

    Input: nums = [4,2,3], k = 1
    Output: 5
    Explanation: Choose index 1 and nums becomes [4,-2,3].

Example 2:

    Input: nums = [3,-1,0,2], k = 3
    Output: 6
    Explanation: Choose indices (1, 2, 2) and nums becomes [3,1,0,2].

Example 3:

    Input: nums = [2,-3,-1,5,-4], k = 2
    Output: 13
    Explanation: Choose indices (1, 4) and nums becomes [2,3,-1,5,4].

Constraints:

- `1 <= nums.length <= 104`
- `-100 <= nums[i] <= 100`
- `1 <= k <= 104`