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# Smallest Integer Divisible by K

## Description

Given a positive integer `K`, you need find 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.

**Example 1:**

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

**Example 2:**

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

**Example 3:**

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

**Note:**

* `1 <= K <= 10^5`

## Solution

```cpp
class Solution {
public:
    int smallestRepunitDivByK(int K) {
        if (K % 2 == 0 || K % 5 == 0)
            return -1;
        for (int r = 0, n = 1; n <= K; ++n) {
            r = (10 * r + 1) % K;
            if (r == 0)
                return n;
        }
        return -1;
    }
};
```

If K is not divisible by 2 or 5, there must be a number N in the form 1111...1 such that K divides N and N $$\le$$ 111...1(K ones).

Proof[: https://leetcode.com/problems/smallest-integer-divisible-by-k/discuss/260916/Proof%3A-we-only-need-to-consider-the-first-K-candidates-in-1-11-111-1111-...](https://leetcode.com/problems/smallest-integer-divisible-by-k/discuss/260916/Proof%3A-we-only-need-to-consider-the-first-K-candidates-in-1-11-111-1111-...)


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