FULL CODE IN PYTHON

Vyasa has to complete a programming assignment overnight. He has to write n lines of code before morning. He is dead tired and he tries drinking some black coffee to keep him awake. But each time he drinks a cup of coffee he stays awake for a short amount of time but his productivity goes down by a constant factor k

This is how he plans to write the program. He will write the first v lines of code, then drink his first cup of coffee. Since his productivity has gone down by a factor of k he will write v // k lines of code. He will have another cup of coffee and then write v // k**2 lines of code. He will have another cup of coffee and write v // k**3 lines of code and so on. He will collapse and fall asleep when v // k ** p becomes 0.

Now Vyasa does want to complete his assignment and maximize on his sleep. So he wants to figure out the minimum allowable value of v for a given productivity factor that will allow him to write at least n lines of code before he falls asleep.

Your input file will be called work.txt. Here is a typical file:

2 7 2 59 9 

The first line is T the number of test cases. This will be followed by T lines of input. Each line of input will have two numbers n and k. n is the number of lines of code to write and k is the productivity factor, where 1 n 10⁶ and 2 k 10.

For each test case your output to the screen will be v lines of code the Vyasa has to write. For the above two test cases, the output will be:

4 54 

You have to modify the binary search algorithm to solve this problem.

Please answer with an original code! Thank you so much!