Given a sequence of static values of length N, a data structure where the preprocessing O(NlogN) allows operations on the upper interval of the sequence to be computed in O(1)
Conditions required for operation
 - <a href="/en/associative%20law">associative law</a> : $(a * b) * c = a * (b * c)$
<ul>
<li>Unit and inverse yuan are not required.</li>
</ul>
There is no need to use this for operations with inverse roots, such as addition.
 - Because we can do the same thing with construction O(N) using <a href="/en/cumulative%20sum">cumulative sum</a>, we can do the same thing with construction O(N).
Cumulative product from left to right&quot; can be used to achieve <a href="/en/obsolete%20rule%20prohibiting%20match-ups%20between%20wrestlers%20from%20the%20same%20group%20of%20stables">obsolete rule prohibiting match-ups between wrestlers from the same group of stables</a>, e.g., by multiplying without inverses.
<ul>
<li>The Disjoint Sparse Table allows the user to compute the product of arbitrary intervals by combining a large number of cumulative products.</li>
</ul>
<a href="https://noshi91.hatenablog.com/entry/2018/05/08/183946">Poem on Disjoint Sparse Table and Seg Trees - noshi91&#39;s note</a>
<a href="/en/Sparse%20Table">Sparse Table</a>
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