<p>You are given an array <code>target</code> of n integers. From a starting array <code>arr</code> consisting of <code>n</code> 1&#39;s, you may perform the following procedure :</p>

<ul>
	<li>let <code>x</code> be the sum of all elements currently in your array.</li>
	<li>choose index <code>i</code>, such that <code>0 &lt;= i &lt; n</code> and set the value of <code>arr</code> at index <code>i</code> to <code>x</code>.</li>
	<li>You may repeat this procedure as many times as needed.</li>
</ul>

<p>Return <code>true</code> <em>if it is possible to construct the</em> <code>target</code> <em>array from</em> <code>arr</code><em>, otherwise, return</em> <code>false</code>.</p>

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

<pre>
<strong>Input:</strong> target = [9,3,5]
<strong>Output:</strong> true
<strong>Explanation:</strong> Start with arr = [1, 1, 1] 
[1, 1, 1], sum = 3 choose index 1
[1, 3, 1], sum = 5 choose index 2
[1, 3, 5], sum = 9 choose index 0
[9, 3, 5] Done
</pre>

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

<pre>
<strong>Input:</strong> target = [1,1,1,2]
<strong>Output:</strong> false
<strong>Explanation:</strong> Impossible to create target array from [1,1,1,1].
</pre>

<p><strong class="example">Example 3:</strong></p>

<pre>
<strong>Input:</strong> target = [8,5]
<strong>Output:</strong> true
</pre>

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

<ul>
	<li><code>n == target.length</code></li>
	<li><code>1 &lt;= n &lt;= 5 * 10<sup>4</sup></code></li>
	<li><code>1 &lt;= target[i] &lt;= 10<sup>9</sup></code></li>
</ul>

class Solution:
  def isPossible(self, target: List[int]) -> bool:
    if len(target) == 1:
      return target[0] == 1

    summ = sum(target)
    maxHeap = [-num for num in target]
    heapq.heapify(maxHeap)

    while -maxHeap[0] > 1:
      mx = -heapq.heappop(maxHeap)
      restSum = summ - mx
      # Only occurs if n == 2.
      if restSum == 1:
        return True
      updated = mx % restSum
      # updated == 0 (invalid) or didn't change.
      if updated == 0 or updated == mx:
        return False
      heapq.heappush(maxHeap, -updated)
      summ = summ - mx + updated

    return True
        
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