This is not a hard algorithm, rather it's a horrible game, hard to understand & poorly explained by the platform.

Precalculating all values in range for the inverse of the function you're actually interested in feels like a weird solution until you realize said inverse grows exponentially . . . I think. Frankly I wasn't very rigorous in my argument to myself that it isn't superexponential.

According to problem statement x>=2 and k>= 1 and k<=x ;

so for example if n=4; coin =0 (initially) 4=>{2,2} since k >=1 left {2} and coin=1^2=1 now 2=>{1,1} i.e. x=2; now take both coin 2^2=4 so answer = 1+4=5 then why 6 in testcase ...

The game isn't explained well ... In the last case H=2 so it's split into 1 and 1 P2 chooses the second tower so how did it become 2^2?

Can anyone elaborate the question and make it clear what it is?