minimum-operations-to-make-array-equal-ii

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Algorithms

You are given two integer arrays <code>nums1</code> and <code>nums2</code> of equal length <code>n</code> and an integer <code>k</code>. You can perform the following operation on <code>nums1</code>:

<ul>
	<li>Choose two indexes <code>i</code> and <code>j</code> and increment <code>nums1[i]</code> by <code>k</code> and decrement <code>nums1[j]</code> by <code>k</code>. In other words, <code>nums1[i] = nums1[i] + k</code> and <code>nums1[j] = nums1[j] - k</code>.</li>
</ul>

<code>nums1</code> is said to be equal to <code>nums2</code> if for all indices <code>i</code> such that <code>0 &lt;= i &lt; n</code>, <code>nums1[i] == nums2[i]</code>.

Return the minimum number of operations required to make <code>nums1</code> equal to <code>nums2</code>. If it is impossible to make them equal, return <code>-1</code>.

&nbsp;
Example 1:

<pre>
Input: nums1 = [4,3,1,4], nums2 = [1,3,7,1], k = 3
Output: 2
Explanation: In 2 operations, we can transform nums1 to nums2.
1st operation: i = 2, j = 0. After applying the operation, nums1 = [1,3,4,4].
2nd operation: i = 2, j = 3. After applying the operation, nums1 = [1,3,7,1].
One can prove that it is impossible to make arrays equal in fewer operations.</pre>

Example 2:

<pre>
Input: nums1 = [3,8,5,2], nums2 = [2,4,1,6], k = 1
Output: -1
Explanation: It can be proved that it is impossible to make the two arrays equal.
</pre>

&nbsp;
Constraints:

<ul>
	<li><code>n == nums1.length == nums2.length</code></li>
	<li><code>2 &lt;= n &lt;= 105</code></li>
	<li><code>0 &lt;= nums1[i], nums2[j] &lt;= 109</code></li>
	<li><code>0 &lt;= k &lt;= 105</code></li>
</ul>