Formatted question description: https://leetcode.ca/all/1015.html

# 1015. Smallest Integer Divisible by K

Medium

## 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

If K is a multiple of 2 or 5, then any number divisible by K can’t end with 1, so return -1.

Otherwise, each time append a 1 to the current number (which is initially 0) and check whether the new number is divisible by K. Use modulo operation to avoid overflow.

class Solution {
public int smallestRepunitDivByK(int K) {
if (K % 2 == 0 || K % 5 == 0)
return -1;
int value = 1;
int length = 1;
while (value % K != 0) {
value = value % K * 10 + 1;
length++;
}
return length;
}
}