sum-of-compatible-numbers-in-range-i

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Algorithms

You are given two integers <code>n</code> and <code>k</code>.

A positive integer <code>x</code> is called compatible if it satisfies both of the following conditions:

<ul>
 <li><code>abs(n - x) &lt;= k</code></li>
 <li><code>(n &amp; x) == 0</code></li>
</ul>

Return the sum of all compatible integers <code>x</code>.

Note:

<ul>
 <li>Here, <code>&amp;</code> denotes the bitwise AND operator.</li>
 <li>The absolute difference between integers <code>i</code> and <code>j</code> is defined as <code>abs(i - j)</code>.</li>
</ul>
&nbsp;
Example 1:

<div class="example-block">
Input: n = 2, k = 3

Output: 10

Explanation:

The compatible integers are:

<ul>
	<li><code>x = 1</code>, since <code>abs(2 - 1) = 1</code> and <code>2 &amp; 1 = 0</code>.</li>
	<li><code>x = 4</code>, since <code>abs(2 - 4) = 2</code> and <code>2 &amp; 4 = 0</code>.</li>
	<li><code>x = 5</code>, since <code>abs(2 - 5) = 3</code> and <code>2 &amp; 5 = 0</code>.</li>
</ul>

Thus, the answer is <code>1 + 4 + 5 = 10</code>.
</div>

Example 2:

<div class="example-block">
Input: n = 5, k = 1

Output: 0

Explanation:

There are no compatible integers in the range <code>[4, 6]</code>. Thus, the answer is 0.
</div>

&nbsp;
Constraints:

<ul>
	<li><code>1 &lt;= n &lt;= 100</code></li>
	<li><code>1 &lt;= k &lt;= 100</code></li>
</ul>