<p>You are given a <strong>0-indexed</strong> array of <code>n</code> integers <code>differences</code>, which describes the <strong>differences </strong>between each pair of <strong>consecutive </strong>integers of a <strong>hidden</strong> sequence of length <code>(n + 1)</code>. More formally, call the hidden sequence <code>hidden</code>, then we have that <code>differences[i] = hidden[i + 1] - hidden[i]</code>.</p>
<p>You are further given two integers <code>lower</code> and <code>upper</code> that describe the <strong>inclusive</strong> range of values <code>[lower, upper]</code> that the hidden sequence can contain.</p>
<ul>
<li>For example, given <code>differences = [1, -3, 4]</code>, <code>lower = 1</code>, <code>upper = 6</code>, the hidden sequence is a sequence of length <code>4</code> whose elements are in between <code>1</code> and <code>6</code> (<strong>inclusive</strong>).
<ul>
<li><code>[3, 4, 1, 5]</code> and <code>[4, 5, 2, 6]</code> are possible hidden sequences.</li>
<li><code>[5, 6, 3, 7]</code> is not possible since it contains an element greater than <code>6</code>.</li>
<li><code>[1, 2, 3, 4]</code> is not possible since the differences are not correct.</li>
</ul>
</li>
</ul>
<p>Return <em>the number of <strong>possible</strong> hidden sequences there are.</em> If there are no possible sequences, return <code>0</code>.</p>
