Aaradhya was hired by Eiffel 65 to design a strong password for a lock for the concert hall at Blue Galaxy. The password has $$$n$$$ digits and each digit can take values from 0 to 9. The password has the following properties:

Let $$$D_i$$$ denote the $$$i$$$-th digit of the password. Note: $$$D_1$$$ can be 0.

• $$$D_1 \lt D_2 \gt D_3 \lt \dots$$$ that is the digits are alternating.
• $$$|D_i - D_{i-1}| \geq k$$$ for all $$$i$$$ from 2 to $$$n$$$. That is the absolute difference between two digits is atleast $$$k$$$ where $$$k \geq 1$$$.

For a given length $$$n$$$ and minimum absolute consecutive difference of digits $$$k$$$ how many passwords Aaradhya can create (generalize)?

Join the $$$Benevolent$$$ discord server to get solutions and more problems!

Till that, enjoy I'm Blue by Eiffel 65