# 1015. Smallest Integer Divisible by K

**Medium**

***

Given a positive integer `k`, you need to find the **length** of the **smallest** positive integer `n` such that `n` is divisible by `k`, and `n` only contains the digit `1`.

Return *the **length** of* `n`. If there is no such `n`, return -1.

**Note:** `n` may not fit in a 64-bit signed integer.

 

**Example 1:**

```
Input: k = 1
Output: 1
Explanation: The smallest answer is n = 1, which has length 1.
```

**Example 2:**

```
Input: k = 2
Output: -1
Explanation: There is no such positive integer n divisible by 2.
```

**Example 3:**

```
Input: k = 3
Output: 3
Explanation: The smallest answer is n = 111, which has length 3.
```

 

**Constraints:**

* `1 <= k <= 105`

```python
class Solution:
    def smallestRepunitDivByK(self, k: int) -> int:
        num = 0
        for i in range(k):
            num = num*10 + 1
            if num%k == 0:
                return len(str(num))
        return -1
```