2640 - Find the Score of All Prefixes of an Array\.

Medium

We define the conversion array conver of an array arr as follows:

• conver[i] = arr[i] + max(arr[0..i]) where max(arr[0..i]) is the maximum value of arr[j] over 0 <= j <= i.

We also define the score of an array arr as the sum of the values of the conversion array of arr.

Given a 0-indexed integer array nums of length n, return an array ans of length n where ans[i] is the score of the prefix nums[0..i].

Example 1:

Input: nums = 2,3,7,5,10

Output: 4,10,24,36,56

Explanation:

For the prefix 2, the conversion array is 4 hence the score is 4

For the prefix 2, 3, the conversion array is 4, 6 hence the score is 10

For the prefix 2, 3, 7, the conversion array is 4, 6, 14 hence the score is 24

For the prefix 2, 3, 7, 5, the conversion array is 4, 6, 14, 12 hence the score is 36

For the prefix 2, 3, 7, 5, 10, the conversion array is 4, 6, 14, 12, 20 hence the score is 56

Example 2:

Input: nums = 1,1,2,4,8,16

Output: 2,4,8,16,32,64

Explanation:

For the prefix 1, the conversion array is 2 hence the score is 2

For the prefix 1, 1, the conversion array is 2, 2 hence the score is 4

For the prefix 1, 1, 2, the conversion array is 2, 2, 4 hence the score is 8

For the prefix 1, 1, 2, 4, the conversion array is 2, 2, 4, 8 hence the score is 16

For the prefix 1, 1, 2, 4, 8, the conversion array is 2, 2, 4, 8, 16 hence the score is 32

For the prefix 1, 1, 2, 4, 8, 16, the conversion array is 2, 2, 4, 8, 16, 32 hence the score is 64

Constraints:

• <code>1 <= nums.length <= 10⁵</code>

• <code>1 <= numsi<= 10⁹</code>