------
## 最终结论
```python
def find_smallest_length(K):
    if K == 1:
        return 1
    
    # Initialize variables
    N = 1  # Start with the number '1'
    length = 1  # Length of the number
    
    while N % K != 0:
        N = N * 10 + 1  # Generate the next number which is '111...1'
        length += 1
        
        if length > K:  # To prevent infinite loops in case no solution exists
            return -1
            
    return length
```