minimize-the-maximum-of-two-arrays

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Algorithms

We have two arrays <code>arr1</code> and <code>arr2</code> which are initially empty. You need to add positive integers to them such that they satisfy all the following conditions:

<ul>
	<li><code>arr1</code> contains <code>uniqueCnt1</code> distinct positive integers, each of which is not divisible by <code>divisor1</code>.</li>
	<li><code>arr2</code> contains <code>uniqueCnt2</code> distinct positive integers, each of which is not divisible by <code>divisor2</code>.</li>
	<li>No integer is present in both <code>arr1</code> and <code>arr2</code>.</li>
</ul>

Given <code>divisor1</code>, <code>divisor2</code>, <code>uniqueCnt1</code>, and <code>uniqueCnt2</code>, return the minimum possible maximum integer that can be present in either array.

&nbsp;
Example 1:

<pre>
Input: divisor1 = 2, divisor2 = 7, uniqueCnt1 = 1, uniqueCnt2 = 3
Output: 4
Explanation: 
We can distribute the first 4 natural numbers into arr1 and arr2.
arr1 = [1] and arr2 = [2,3,4].
We can see that both arrays satisfy all the conditions.
Since the maximum value is 4, we return it.
</pre>

Example 2:

<pre>
Input: divisor1 = 3, divisor2 = 5, uniqueCnt1 = 2, uniqueCnt2 = 1
Output: 3
Explanation: 
Here arr1 = [1,2], and arr2 = [3] satisfy all conditions.
Since the maximum value is 3, we return it.</pre>

Example 3:

<pre>
Input: divisor1 = 2, divisor2 = 4, uniqueCnt1 = 8, uniqueCnt2 = 2
Output: 15
Explanation: 
Here, the final possible arrays can be arr1 = [1,3,5,7,9,11,13,15], and arr2 = [2,6].
It can be shown that it is not possible to obtain a lower maximum satisfying all conditions. 
</pre>

&nbsp;
Constraints:

<ul>
	<li><code>2 &lt;= divisor1, divisor2 &lt;= 105</code></li>
	<li><code>1 &lt;= uniqueCnt1, uniqueCnt2 &lt; 109</code></li>
	<li><code>2 &lt;= uniqueCnt1 + uniqueCnt2 &lt;= 109</code></li>
</ul>