<p>You are given an integer array <code>nums</code> sorted in <strong>non-decreasing</strong> order.</p>

<p>Build and return <em>an integer array </em><code>result</code><em> with the same length as </em><code>nums</code><em> such that </em><code>result[i]</code><em> is equal to the <strong>summation of absolute differences</strong> between </em><code>nums[i]</code><em> and all the other elements in the array.</em></p>

<p>In other words, <code>result[i]</code> is equal to <code>sum(|nums[i]-nums[j]|)</code> where <code>0 &lt;= j &lt; nums.length</code> and <code>j != i</code> (<strong>0-indexed</strong>).</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> nums = [2,3,5]
<strong>Output:</strong> [4,3,5]
<strong>Explanation:</strong> Assuming the arrays are 0-indexed, then
result[0] = |2-2| + |2-3| + |2-5| = 0 + 1 + 3 = 4,
result[1] = |3-2| + |3-3| + |3-5| = 1 + 0 + 2 = 3,
result[2] = |5-2| + |5-3| + |5-5| = 3 + 2 + 0 = 5.
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> nums = [1,4,6,8,10]
<strong>Output:</strong> [24,15,13,15,21]
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>2 &lt;= nums.length &lt;= 10<sup>5</sup></code></li>
	<li><code>1 &lt;= nums[i] &lt;= nums[i + 1] &lt;= 10<sup>4</sup></code></li>
</ul>

class Solution:
    def getSumAbsoluteDifferences(self, nums: List[int]) -> List[int]:
        
        N = len(nums)
        for i in range(1, N): nums[i] += nums[i-1]

        res = [0 for _ in range(N)]
        res[0] =  (nums[-1] - nums[0]) - nums[0]*(N-1)
        v = 0

        for i in range(1, N):
            v = nums[i] - nums[i-1]
            res[i] = abs(i*v - nums[i-1]) + abs( (N-1-i)*v - (nums[-1] - nums[i]) )

        return res

        


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