preimage-size-of-factorial-zeroes-function

Preimage Size of Factorial Zeroes Function

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preimageSizeFZF

Let <code>f(x)</code> be the number of zeroes at the end of <code>x!</code>. Recall that <code>x! = 1 * 2 * 3 * ... * x</code> and by convention, <code>0! = 1</code>.

<ul>
	<li>For example, <code>f(3) = 0</code> because <code>3! = 6</code> has no zeroes at the end, while <code>f(11) = 2</code> because <code>11! = 39916800</code> has two zeroes at the end.</li>
</ul>

Given an integer <code>k</code>, return the number of non-negative integers <code>x</code> have the property that <code>f(x) = k</code>.

&nbsp;
Example 1:

<pre>
Input: k = 0
Output: 5
Explanation: 0!, 1!, 2!, 3!, and 4! end with k = 0 zeroes.
</pre>

Example 2:

<pre>
Input: k = 5
Output: 0
Explanation: There is no x such that x! ends in k = 5 zeroes.
</pre>

Example 3:

<pre>
Input: k = 3
Output: 5
</pre>

&nbsp;
Constraints:

<ul>
	<li><code>0 &lt;= k &lt;= 109</code></li>
</ul>

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