smallest-all-ones-multiple

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Algorithms

You are given a positive integer <code>k</code>.

Find the smallest integer <code>n</code> divisible by <code>k</code> that consists of only the digit 1 in its decimal representation (e.g., 1, 11, 111, ...).

Return an integer denoting the number of digits in the decimal representation of <code>n</code>. If no such <code>n</code> exists, return <code>-1</code>.

&nbsp;
Example 1:

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

Output: 3

Explanation:

<code>n = 111</code> because 111 is divisible by 3, but 1 and 11 are not. The length of <code>n = 111</code> is 3.
</div>

Example 2:

<div class="example-block">
Input: k = 7

Output: 6

Explanation:

<code>n = 111111</code>. The length of <code>n = 111111</code> is 6.
</div>

Example 3:

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

Output: -1

Explanation:

There does not exist a valid <code>n</code> that is a multiple of 2.
</div>

&nbsp;
Constraints:

<ul>
	<li><code>2 &lt;= k &lt;= 105</code></li>
</ul>