### Find the Score of All Prefixes of an Array

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:**

- `1 <= nums.length <= 10^5`
- `1 <= nums[i] <= 10^9`

**Function definition**

```
class Solution:
    def findPrefixScore(self, nums: List[int]) -> List[int]:
        
```

