You are given a $0$ indexed integer array stations of length n, where stations[i] denotes the number of power stations in the $i^{ ext{th}}$ city.

Each power station provides power to every city within a distance of r. That is, a power station at city j provides electricity to city i if $|i - j| \leq$ r.

The total power of a city is the sum of all power stations that can provide electricity to it.

You are also given two integers r and k. You may construct at most k additional power stations in any of the cities.

Return the maximum possible minimum power among all cities after optimally adding at most k additional power stations.

Constraints:

• n == stations.length

• $1 \leq$ n $\leq 10^5$

• $0 \leq$ stations[i] $\leq 10^5$

• $0 \leq$ r $\leq$ n $- 1$

• $0 \leq$ k $\leq 10^9$

Now, let’s take a moment to make sure you’ve correctly understood the problem. The quiz below helps you check if you’re solving the correct problem:

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Implement your solution in the following coding playground.