# leetcode\_1015

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

## Solutions

1. **math**
2. reference: <https://leetcode-cn.com/problems/smallest-integer-divisible-by-k/solution/javajie-fa-yi-ji-zheng-ming-de-si-lu-by-jiangzk/>
3. If `K % 2 != 0 && K % 5 != 0`, there must be an answer.

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

        return len;
    }
};
```