Kata

This clicker game is destroying my thumbs!

I'm way too lazy to play this...

That's it: from now on, I refuse to click the screen any more than strictly necessary.

Rules

• Your starting balance is 0 cash. Your starting cpc is up.
• A single click gains you cpc cash.
• You may spend cpc^3 cash to upgrade. This increases your cpc by up and can be done any number of times.
• Upgrading requires a click!

Task

• Function parameters are non-negative integers up and goal.
• Return the minimum number of clicks required to reach the cash goal, as an integer. If this is impossible, return -1.
• Spent cash does not compound to the goal: the goal is reached when your current balance is at least as much as the goal.

Examples

clicker_solver(up = 2, goal = 6) --> 3

• Click 3 times, gaining 6 cash.

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clicker_solver(up = 2, goal = 24) --> 11

• Click 4 times, gaining 8 cash.
• Buy upgrade (this entails a click): cpc increases to 4, no cash left.
• Click 6 times, gaining 24 cash.

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clicker_solver(up = 5, goal = 3030) --> 329

• Click 25 times, gaining 125 cash.
• Buy upgrade (this entails a click): cpc increases to 10, no cash left.
• Click 100 times, gaining 1000 cash.
• Buy upgrade (this entails a click): cpc increases to 15, no cash left.
• Click 202 times, gaining 3030 cash.

Alternative solution: instead of buying the second upgrade, click 203 more times.

Performance

• Approx. 600 cases from the test suite also evaluate performance: up ranges from 2 to 40 and goal goes up to 10^10!
• The reference solution executes with O(log n) taking less than 1s.