Cracking the Safe

753. Cracking the Safe

There is a safe protected by a password. The password is a sequence of n digits where each digit can be in the range [0, k - 1].

The safe has a peculiar way of checking the password. When you enter in a sequence, it checks the most recent n digits that were entered each time you type a digit.

• For example, the correct password is "345" and you enter in "012345":

  <ul>
  	<li>After typing <code>0</code>, the most recent <code>3</code> digits is <code>"0"</code>, which is incorrect.</li>
  	<li>After typing <code>1</code>, the most recent <code>3</code> digits is <code>"01"</code>, which is incorrect.</li>
  	<li>After typing <code>2</code>, the most recent <code>3</code> digits is <code>"012"</code>, which is incorrect.</li>
  	<li>After typing <code>3</code>, the most recent <code>3</code> digits is <code>"123"</code>, which is incorrect.</li>
  	<li>After typing <code>4</code>, the most recent <code>3</code> digits is <code>"234"</code>, which is incorrect.</li>
  	<li>After typing <code>5</code>, the most recent <code>3</code> digits is <code>"345"</code>, which is correct and the safe unlocks.</li>
  </ul>
  </li>
  

Return any string of minimum length that will unlock the safe at some point of entering it.

 

Example 1:

Input: n = 1, k = 2
Output: "10"
Explanation: The password is a single digit, so enter each digit. "01" would also unlock the safe.

Example 2:

Input: n = 2, k = 2
Output: "01100"
Explanation: For each possible password:
- "00" is typed in starting from the 4th digit.
- "01" is typed in starting from the 1st digit.
- "10" is typed in starting from the 3rd digit.
- "11" is typed in starting from the 2nd digit.
Thus "01100" will unlock the safe. "01100", "10011", and "11001" would also unlock the safe.

 

Constraints:

• 1 <= n <= 4
• 1 <= k <= 10
• 1 <= kn <= 4096