Olympics

Weightlifting competitions at the Olympic Games are about to begin — it is time to impress your fans!

To perform a sequence of lifting attempts, you are given a constant strength $S$ and a decreasing energy reserve $E$.

For each attempt, you may choose any positive (not necessarily integer) weight $W$.

• If S \ge W, the lift is successful, and your energy decreases by E_{succ}.

• If S < W, the attempt fails, and your energy decreases by E_{fail}.

You may continue making attempts while E > 0.

As soon as E \le 0, no further attempts can be made.

Your result is the maximum weight (in kilograms) that you successfully lift, or $0$ if all attempts fail.

Ideally, you would lift exactly at your strength limit. However, the exact value of $S$ is unknown to you. You only know that you can certainly lift an Olympic barbell weighing $25$ kg, and that the maximum possible weight is $225$ kg (i.e., up to $100$ kg of plates on each side plus the bar).

How close to the optimal result can you guarantee to get? In other words, find the minimum value $d$ such that you can guarantee a result of at least S - d.